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Derive a global optimal solution as an exogenous variable changes?

Shaoyan Robert
Posted 5 years ago

Hi, everyone

I have an very tedious optimization problem. I can find the global optimal solution if all the exogenous variables are assigned, just as follows:

Clear["`*"];
L = 1; H = 3; B = 2; \[Alpha] = 1/10;
\[Eta]1a = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - \((p1 - L)\)\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)); \[Eta]2a = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(p2\), \(H\)], 1], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(p2\), \(L\)], 1], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)); \[Eta]3a = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[Max[
\*FractionBox[\(H*\[Eta]2a - p1*\[Eta]2a + p2\), \(H\)], 1], B]\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[Max[
\*FractionBox[\(L*\[Eta]2a - p1*\[Eta]2a + p2\), \(L\)], 1], B]\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)); \[Eta]1b = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - L)\)\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\)) + (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\)); \[Eta]2b = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(p2\), \(H\)], 1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(p2\), \(L\)], 1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\)); \[Eta]3b = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[Max[
\*FractionBox[\(H*\[Eta]2b - p1*\[Eta]2b + p2\), \(H\)], 1], g]\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[Max[
\*FractionBox[\(L*\[Eta]2b - p1*\[Eta]2b + p2\), \(L\)], 1], g]\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)); \[Eta]11c = \[Eta]21c = \
\[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Mu]11c = \[Mu]21c = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Eta]1c = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], 1], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(p2\), \(L\)], 1], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Mu]1c = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); \[Eta]01d = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(p2\), \(H\)], 1], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]11d = \[Eta]21d = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Mu]11d = \[Mu]21d = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); y1d = \[Mu]11d + \[Eta]11d; \
\[Eta]1d = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - y1d*\((p1 - H)\)\), \(H\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Mu]1d = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - y1d*\((p1 - H)\)\), \(H\)], B]\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); \[Eta]1f = \[Eta]21f = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[1, 
\*FractionBox[\(p2\), \(H\)]], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[1, 
\*FractionBox[\(p2\), \(L\)]], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Eta]11h = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[1, 
\*FractionBox[\(p2\), \(H\)]], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[1, 
\*FractionBox[\(p2\), \(L\)]], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Eta]21h = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Mu]21h = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); y2h = \[Eta]21h + \[Mu]21h; \[Mu]1h \
= \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11h + p2*y2h\), \(H*y2h\)], 1], 
     B]\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); \[Eta]1h = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11h + p2*y2h\), \(H*y2h\)], 1], 
       B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\)); \[Eta]11j = \[Eta]21j = \
\[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Mu]11j = \[Mu]21j = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Eta]1j = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Mu]1j = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); \[Eta]1k = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - y1k*\((p1 - H)\)\), \(H\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]01k = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(p2\), \(H\)], 1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); y1k = \[Mu]11k + \[Eta]11k;
\[Eta]11k = \[Eta]21k = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Mu]11k = \[Mu]21k = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Mu]1k = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - y1k*\((p1 - H)\)\), \(H\)], g]\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); \[Eta]1m = \[Eta]21m = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Eta]11O = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]21O = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Mu]21O = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); y2O = \[Eta]21O + \[Mu]21O; \
\[Eta]1O = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11O + p2*y2O\), \(H*y2O\)], 
      1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Mu]1O = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11O + p2*y2O\), \(H*y2O\)], 1]\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); \[Eta]11P = \[Eta]21P = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Mu]11P = \[Mu]21P = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Eta]1P = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); \[Mu]1P = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); \[Eta]1q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - y1q*\((p1 - H)\)\), \(H\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]01q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(p2\), \(H\)], 1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); y1q = \[Mu]11q + \[Eta]11q;
\[Eta]11q = \[Eta]21q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Mu]11q = \[Mu]21q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Mu]1q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - y1q*\((p1 - H)\)\), \(H\)], g]\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); \[Eta]1r = \[Eta]21r = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Eta]11s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]21s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Mu]21s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); y2s = \[Eta]21s + \[Mu]21s; \
\[Eta]1s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11s + p2*y2s\), \(H*y2s\)], 
      1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); \[Mu]1s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11s + p2*y2s\), \(H*y2s\)], 1]\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
k72 = Maximize[{(p1 + p2)*\[Mu]1s*\[Eta]11s + 
     2*p2*\[Eta]1s*\[Eta]21s + (p2 + p1)*\[Eta]1s*\[Mu]21s, 
    H > L > 0 && 1 < g <= B && H >= p1 >= L && p2/g <= L && 
     g*p1 >= p2 >= p1}, {p1, p2, g}];
k62 = Maximize[{2*p2*\[Eta]1r*\[Eta]21r, 
    H > L > 0 && B >= g > 1 && L <= p2 <= g*L}, {p2, g}];
k52 = Maximize[{2*
      p1*\[Mu]1q*\[Mu]11q + (p1 + p2)*\[Eta]1q*\[Mu]21q + (p1 + 
        p2)*\[Mu]1q*\[Eta]11q + 2*p2*\[Eta]1q*\[Eta]21q + 
     p2*\[Eta]1q*(1 - \[Mu]21q - \[Eta]21q) + 
     p2*(1 - \[Mu]1q - \[Eta]1q)*\[Eta]01q, 
    H > L > 0 && 1 < g <= B && p1 <= p2 && 2*p1 <= p2 <= g*p1 <= g*H &&
      H >= p1 >= L && p2/g <= L}, {p1, p2, g}];
k42 = Maximize[{2*
      p1*\[Mu]1P*\[Mu]11P + (p1 + p2)*\[Eta]1P*\[Mu]21P + (p1 + 
        p2)*\[Mu]1P*\[Eta]11P + 2*p2*\[Eta]1P*\[Eta]21P, 
    H > L > 0 && 1 < g <= B && p1 <= p2 <= 2*p1 && H >= p1 >= L && 
     p2/g <= L}, {p1, p2, g}];
k7 = Maximize[{(p1 + p2)*\[Mu]1O*\[Eta]11O + 
     2*p2*\[Eta]1O*\[Eta]21O + (p2 + p1)*\[Eta]1O*\[Mu]21O, 
    H > L > 0 && 1 < g <= B && H >= p1 >= L && L <= p2/g <= H && 
     g*p1 >= p2 >= p1}, {p1, p2, g}];
k6 = Maximize[{2*p2*\[Eta]1m*\[Eta]21m, 
    H > L > 0 && B >= g > 1 && L <= p2/g <= H}, {p2, g}];
k5 = Maximize[{2*
      p1*\[Mu]1k*\[Mu]11k + (p1 + p2)*\[Eta]1k*\[Mu]21k + (p1 + 
        p2)*\[Mu]1k*\[Eta]11k + 2*p2*\[Eta]1k*\[Eta]21k + 
     p2*\[Eta]1k*(1 - \[Mu]21k - \[Eta]21k) + 
     p2*(1 - \[Mu]1k - \[Eta]1k)*\[Eta]01k, 
    H > L > 0 && 1 < g <= B && p1 <= p2 && 2*p1 <= p2 <= g*p1 <= g*H &&
      H >= p1 >= L && L <= p2/g <= H}, {p1, p2, g}];
k4 = Maximize[{2*
      p1*\[Mu]1j*\[Mu]11j + (p1 + p2)*\[Eta]1j*\[Mu]21j + (p1 + 
        p2)*\[Mu]1j*\[Eta]11j + 2*p2*\[Eta]1j*\[Eta]21j, 
    H > L > 0 && 1 < g <= B && p1 <= p2 <= 2*p1 && H >= p1 >= L && 
     L <= p2/g <= H}, {p1, p2, g}];
y7 = Maximize[{(p1 + p2)*\[Mu]1h*\[Eta]11h + 
     2*p2*\[Eta]1h*\[Eta]21h + (p2 + p1)*\[Eta]1h*\[Mu]21h, 
    H > L > 0 && g >= B > 1 && p1 <= p2 < g*p1 <= g*H && 
     L <= p1 <= H && p2 <= B*H}, {p1, p2, g}];
y6 = Maximize[{2*p2*\[Eta]1f*\[Eta]21f, 
    H > L > 0 && g >= B > 1 && L <= p2 <= B*H}, {p2, g}];
y5 = Maximize[{2*
      p1*\[Mu]1d*\[Mu]11d + (p1 + p2)*\[Eta]1d*\[Mu]21d + (p1 + 
        p2)*\[Mu]1d*\[Eta]11d + 2*p2*\[Eta]1d*\[Eta]21d + 
     p2*\[Eta]1d*(1 - \[Mu]21d - \[Eta]21d) + 
     p2*(1 - \[Mu]1d - \[Eta]1d)*\[Eta]01d, 
    H > L > 0 && g >= B > 1 && p1 <= p2 && 2*p1 <= p2 <= g*p1 <= g*H &&
      H >= p1 >= L}, {p1, p2, g}];
y4 = Maximize[{2*
      p1*\[Mu]1c*\[Mu]11c + (p1 + p2)*\[Eta]1c*\[Mu]21c + (p1 + 
        p2)*\[Mu]1c*\[Eta]11c + 2*p2*\[Eta]1c*\[Eta]21c, 
    H > L > 0 && g >= B > 1 && p1 <= p2 <= 2*p1 && H >= p1 >= L}, {p1,
     p2, g}];
k1 = Maximize[{2*p1*(1 - \[Eta]1b)^2 + 
     2*(p1 + p2)*\[Eta]1b*(1 - \[Eta]1b) + 2*p2*(\[Eta]1b)^2, 
    H > L > 0 && 1 < g <= B && 0 < p1 <= L && g*p1 >= p2 >= p1}, {p1, 
    p2, g}];
k2 = Maximize[{2*p2*(\[Eta]2b)^2, 
    H > L > 0 && 1 < g <= B && 0 < p2 <= B*H && p2 <= g*L}, {p2, g}];
k3 = Maximize[{(p1 + p2)*\[Eta]3b*\[Eta]2b + 
     2*p2*(1 - \[Eta]3b)*\[Eta]1b + (p2 + 
        p1)*(1 - \[Eta]3b)*(1 - \[Eta]1b), 
    H > L > 0 && 1 < g <= B && 0 < p1 <= L && g*p1 >= p2 >= p1}, {p1, 
    p2, g}];
y1 = Maximize[{2*p1*(1 - \[Eta]1a)^2 + 
     2*(p1 + p2)*\[Eta]1a*(1 - \[Eta]1a) + 2*p2*(\[Eta]1a)^2, 
    H > L > 0 && g >= B > 1 && 0 < p1 <= L && g*p1 >= p2 >= p1}, {p1, 
    p2, g}];
y2 = Maximize[{2*p2*(\[Eta]2a)^2, 
    H > L > 0 && g >= B > 1 && 0 < p2 <= B*H && p2 <= g*L}, {p2, g}];
y3 = Maximize[{(p1 + p2)*\[Eta]3a*\[Eta]2a + 
     2*p2*(1 - \[Eta]3a)*\[Eta]1a + (p2 + 
        p1)*(1 - \[Eta]3a)*(1 - \[Eta]1a), 
    H > L > 0 && g >= B > 1 && 0 < p1 <= L && g*p1 >= p2 >= p1}, {p1, 
    p2, g}];
Y1 = N[y1];
Print["y1=", Y1]
Y2 = N[y2];
Print["y2=", Y2]
Y3 = N[y3];
Print["y3=", Y3]
Y4 = N[k1];
Print["k1=", Y4]
Y5 = N[k2];
Print["k2=", Y5]
Y6 = N[k3];
Print["k3=", Y6]
Y7 = N[y4];
Print["y4=", Y7]
Y8 = N[y5];
Print["y5=", Y8]
Y9 = N[y6];
Print["y6=", Y9]
Y10 = N[y7];
Print["y7=", Y10]
Y11 = N[k4];
Print["k4=", Y11]
Y12 = N[k5];
Print["k5=", Y12]
Y13 = N[k6];
Print["k6=", Y13]
Y14 = N[k7];
Print["k7=", Y14]
Y15 = N[k42];
Print["k42=", Y15]
Y16 = N[k52];
Print["k52=", Y16]
Y17 = N[k62];
Print["k62=", Y17]
Y18 = N[k72];
Print["k72=", Y18]
Q = N[{y1, y2, y3, k1, k2, k3, y4, y5, y6, y7, k4, k5, k6, k7, k42, 
   k52, k62, k72}]
Print["Ymax=", MaximalBy[Q, First]]

My question is how to change above to derive the result if B (B changes from 2 to 10) or alpha (alpha changes from 0.1~0.95) changes and draw a line between B (or alpha) and Ymax (and p1, p2, g)? Could you please tell me how to use loop to realize it. Thank you very much!
POSTED BY: Shaoyan Robert
15 Replies
Sort By:
Rohit Namjoshi
Rohit Namjoshi
Posted 5 years ago

Please post code in InputForm, it is much easier to read. Looks like the only difference in the two code samples is p1r, p2r, gr as a single element list vs. a two element list. Those values are passed to e.g. ?1q[p1r, p2r, gr]. Compare the result of that function when passed the two different sets of values. 

Clear["`*"]; 
L = 1; H = 2; ? = 1/10; 

?1q[p1_, p2_, g_] = ?*Integrate[1/(B - 1), {x, Min[(p2 - y1q*(p1 - H))/H, g], g}] + 
       (1 - ?)*Integrate[1/(B - 1), {x, p2/L, g}] + Integrate[1/(B - 1), {x, g, B}]; 

?01q[p2_, g_] = ?*Integrate[1/(B - 1), {x, Max[p2/H, 1], g}] +
   (1 - ?)*Integrate[1/(B - 1), {x, Min[p2/L, g], g}] + 
   Integrate[1/(B - 1), {x, g, B}];

y1q = ?11q[p1, p2] + ?11q[p1, p2, g]; 

?11q[p1_, p2_, g_] = ?*Integrate[1/(B - 1), {x, (p2 - (p1 - H))/H, g}] +
   (1 - ?)*Integrate[1/(B - 1), {x, Min[p2/L, g], g}] + 
   Integrate[1/(B - 1), {x, g, B}];

?21q[p1_, p2_, g_] = ?*Integrate[1/(B - 1), {x, (p2 - (p1 - H))/H, g}] +
   (1 - ?)*Integrate[1/(B - 1), {x, Min[p2/L, g], g}] + 
   Integrate[1/(B - 1), {x, g, B}]; 

?11q[p1_, p2_] = ?*Integrate[1/(B - 1), {x, 1, (p2 - (p1 - H))/H}];

?21q[p1_, p2_] = ?*Integrate[1/(B - 1), {x, 1, (p2 - (p1 - H))/H}];

?1q[p1_, p2_, g_] = ?*Integrate[1/(B - 1), {x, 1, Min[(p2 - y1q*(p1 - H))/H, g]}]; 

?1r[p2_, g_] = ?*Integrate[1/(B - 1), {x, Max[1, p2/H], g}] +
   (1 - ?)*Integrate[1/(B - 1), {x, p2/L, g}] + Integrate[1/(B - 1), {x, g, B}]; 

?21r[p2_, g_] = ?*Integrate[1/(B - 1), {x, Max[1, p2/H], g}] +
   (1 - ?)*Integrate[1/(B - 1), {x, p2/L, g}] + Integrate[1/(B - 1), {x, g, B}]; 

?11s[p2_, g_] = ?*Integrate[1/(B - 1), {x, Max[1, p2/H], g}] +
   (1 - ?)*Integrate[1/(B - 1), {x, Min[p2/L, g], g}] + Integrate[1/(B - 1), {x, g, B}];

?21s[p1_, p2_, g_] = ?*Integrate[1/(B - 1), {x, (p2 - (p1 - H))/H, g}] +
   (1 - ?)*Integrate[1/(B - 1), {x, Min[p2/L, g], g}] + Integrate[1/(B - 1), {x, g, B}]; 

?21s[p1_, p2_] = ?*Integrate[1/(B - 1), {x, 1, (p2 - (p1 - H))/H}]; 

y2s = ?21s[p1, p2, g] + ?21s[p1, p2];

?1s[p1_, p2_, g_] =
 ?*Integrate[1/(B - 1), {x, Max[((H - p1)*?11s[p2, g] + p2*y2s)/(H*y2s), 1], g}] +
  (1 - ?)*Integrate[1/(B - 1), {x, Min[p2/L, g], g}] + Integrate[1/(B - 1), {x, g, B}];

?1s[p1_, p2_] = ?*Integrate[1/(B - 1), {x, 1, Max[((H - p1)*?11s[p2, g] + p2*y2s)/(H*y2s), 1]}];

p1r = {2, 3}
p2r = {5, 4}
gr = {6, 7}

Q3r = N[ParallelTable[?1q[p1r, p2r, gr]*?11q[p1r, p2r] + ?1q[p1r, p2r, gr]*?21q[p1r, p2r] + 
         ?1q[p1r, p2r, gr]*?11q[p1r, p2r, gr] + ?1q[p1r, p2r, gr]*?21q[p1r, p2r, gr] + 
         ?1q[p1r, p2r, gr]*(1 - ?21q[p1r, p2r] - ?21q[p1r, p2r, gr]) + 
         (1 - ?1q[p1r, p2r, gr] - ?1q[p1r, p2r, gr])*?01q[p2r, gr], {B, 3, 5}]]
POSTED BY: Rohit Namjoshi
Shaoyan Robert
Shaoyan Robert
Posted 5 years ago

This example is exactly the same to my above question. 

Clear["`*"];
Q[x_] = 2*x^2;
Z = Maximize[{x - 2 y + Q[x], x^2 + y^2 <= 1}, {x, y}]
x1 = Z[[2, 1, 2]]
y1 = Z[[2, 2, 2]]
N[x1 - 2*y1 + Q[x1]]

It works, but if we take this method to solve my question, it runs very slow. I afraid it is not a good way to solve this kind of problem.
POSTED BY: Shaoyan Robert
Rohit Namjoshi
Rohit Namjoshi
Posted 5 years ago

Do you know what part of the computation is slow? If it is the Maximize that is slow, one thing you can try is to replace Table with ParallelTable. With that change the code to generate the plots completes in ~18s on my machine using 3 kernels.
POSTED BY: Rohit Namjoshi
Shaoyan Robert
Shaoyan Robert
Posted 5 years ago

Thank you! It runs faster now. In addition, I have a solution to my original question. That is,

Clear["`*"];
L = 1; H = 2; \[Alpha] = 1/10;
\[Eta]1q[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - y1q*\((p1 - H)\)\), \(H\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]01q[p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(p2\), \(H\)], 1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); y1q = \[Mu]11q[
   p1, p2] + \[Eta]11q[p1, p2, g];
\[Eta]11q[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]21q[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Mu]11q[p1_, 
  p2_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Mu]21q[p1_, 
  p2_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Mu]1q[p1_, 
  p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - y1q*\((p1 - H)\)\), \(H\)], g]\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Eta]1r[p2_, 
  g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Eta]21r[p2_, 
  g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Eta]11s[p2_, 
  g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]21s[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Mu]21s[p1_, p2_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); y2s = \[Eta]21s[p1, p2, 
   g] + \[Mu]21s[p1, p2]; \[Eta]1s[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11s[p2, g] + p2*y2s\), \(H*y2s\)], 
      1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Mu]1s[p1_, 
  p2_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11s[p2, g] + p2*y2s\), \(H*y2s\)], 
     1]\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
Q1 = ParallelTable[
   N[Maximize[{(p1 + p2)*\[Mu]1s[p1, p2]*\[Eta]11s[p2, g] + 
       2*p2*\[Eta]1s[p1, p2, g]*\[Eta]21s[p1, p2, 
         g] + (p2 + p1)*\[Eta]1s[p1, p2, g]*\[Mu]21s[p1, p2], 
      H > L > 0 && 1 < g <= B && H >= p1 >= L && p2/g <= L && 
       g*p1 >= p2 >= p1}, {p1, p2, g}]], {B, 3, 5}];
Print["k72=", Q1]
Q2 = ParallelTable[
   N[Maximize[{2*p2*\[Eta]1r[p2, g]*\[Eta]21r[p2, g], 
      H > L > 0 && B >= g > 1 && L <= p2 <= g*L}, {p2, g}]], {B, 3, 
    5}];
Print["k62=", Q2]
Q3 = ParallelTable[
   N[Maximize[{2*
        p1*\[Mu]1q[p1, p2, g]*\[Mu]11q[p1, p2] + (p1 + p2)*\[Eta]1q[
         p1, p2, g]*\[Mu]21q[p1, p2] + (p1 + p2)*\[Mu]1q[p1, p2, 
         g]*\[Eta]11q[p1, p2, g] + 
       2*p2*\[Eta]1q[p1, p2, g]*\[Eta]21q[p1, p2, g] + 
       p2*\[Eta]1q[p1, p2, 
         g]*(1 - \[Mu]21q[p1, p2] - \[Eta]21q[p1, p2, g]) + 
       p2*(1 - \[Mu]1q[p1, p2, g] - \[Eta]1q[p1, p2, g])*\[Eta]01q[p2,
          g], H > L > 0 && 1 < g <= B && p1 <= p2 && 
       2*p1 <= p2 <= g*p1 <= g*H && H >= p1 >= L && p2/g <= L}, {p1, 
      p2, g}]], {B, 3, 5}];
Print["k52=", Q3]
q = N[{Q1, Q2, Q3}]
q3 = Transpose[{Q1, Q2, Q3}]
cycg = MaximalBy[#, First] & /@ q3
cycg2 = MinimalBy[#, Last] & /@ cycg
p1r = Flatten[cycg2[[All, All, 2, 1, 2]]]
p2r = Flatten[cycg2[[All, All, 2, 2, 2]]]
gr = Flatten[cycg2[[All, All, 2, 3, 2]]]
Q3r = ParallelTable[\[Mu]1q[p1r, p2r, gr]*\[Mu]11q[p1r, 
     p2r] + \[Eta]1q[p1r, p2r, gr]*\[Mu]21q[p1r, p2r] + \[Mu]1q[p1r, 
     p2r, gr]*\[Eta]11q[p1r, p2r, gr] + \[Eta]1q[p1r, p2r, 
     gr]*\[Eta]21q[p1r, p2r, gr] + \[Eta]1q[p1r, p2r, 
     gr]*(1 - \[Mu]21q[p1r, p2r] - \[Eta]21q[p1r, p2r, 
       gr]) + (1 - \[Mu]1q[p1r, p2r, gr] - \[Eta]1q[p1r, p2r, 
       gr])*\[Eta]01q[p2r, gr], {B, 3, 5}]

However, the only problem is that the result of Q3r is not right. What I want to do is to assign the optimal values (p1=1,p2=2.5, p3=0.783833, when B=3; p1=1.06588,p2=2.13176, p3=3.125, when B=4; p1=1.33242,p2=2.66484, p3=3.75, when B=5; ) (p1 is p1r) to Q3r. That is, this result should be a list including 3 numbers. But the result what I obtain now is 

{{0.783833, 0.756165, 0.644231}, {0.903176, 0.890879, 
  0.841131}, {0.945325, 0.938409, 0.910425}}

which is obviously wrong.

POSTED BY: Shaoyan Robert
Shaoyan Robert
Shaoyan Robert
Posted 5 years ago

Above question may be solved if we figure out the difference of the following two programmings : Programming (1)

Clear["`*"];
L = 1; H = 2; \[Alpha] = 1/10;
\[Eta]1q[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - y1q*\((p1 - H)\)\), \(H\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]01q[p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(p2\), \(H\)], 1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); y1q = \[Mu]11q[
   p1, p2] + \[Eta]11q[p1, p2, g];
\[Eta]11q[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]21q[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Mu]11q[p1_, 
  p2_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Mu]21q[p1_, 
  p2_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Mu]1q[p1_, 
  p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - y1q*\((p1 - H)\)\), \(H\)], g]\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Eta]1r[p2_, 
  g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Eta]21r[p2_, 
  g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Eta]11s[p2_, 
  g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]21s[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Mu]21s[p1_, p2_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); y2s = \[Eta]21s[p1, p2, 
   g] + \[Mu]21s[p1, p2]; \[Eta]1s[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11s[p2, g] + p2*y2s\), \(H*y2s\)], 
      1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Mu]1s[p1_, 
  p2_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11s[p2, g] + p2*y2s\), \(H*y2s\)], 
     1]\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
p1r = {2, 3}
p2r = {5, 4}
gr = {6, 7}
Q3r = N[ParallelTable[\[Mu]1q[p1r, p2r, gr]*\[Mu]11q[p1r, 
      p2r] + \[Eta]1q[p1r, p2r, gr]*\[Mu]21q[p1r, p2r] + \[Mu]1q[p1r, 
      p2r, gr]*\[Eta]11q[p1r, p2r, gr] + \[Eta]1q[p1r, p2r, 
      gr]*\[Eta]21q[p1r, p2r, gr] + \[Eta]1q[p1r, p2r, 
      gr]*(1 - \[Mu]21q[p1r, p2r] - \[Eta]21q[p1r, p2r, 
        gr]) + (1 - \[Mu]1q[p1r, p2r, gr] - \[Eta]1q[p1r, p2r, 
        gr])*\[Eta]01q[p2r, gr], {B, 3, 5}]]

Programming (2)

Clear["`*"];
L = 1; H = 2; \[Alpha] = 1/10;
\[Eta]1q[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - y1q*\((p1 - H)\)\), \(H\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]01q[p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(p2\), \(H\)], 1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); y1q = \[Mu]11q[
   p1, p2] + \[Eta]11q[p1, p2, g];
\[Eta]11q[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]21q[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Mu]11q[p1_, 
  p2_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Mu]21q[p1_, 
  p2_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Mu]1q[p1_, 
  p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - y1q*\((p1 - H)\)\), \(H\)], g]\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Eta]1r[p2_, 
  g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Eta]21r[p2_, 
  g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Eta]11s[p2_, 
  g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]21s[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Mu]21s[p1_, p2_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); y2s = \[Eta]21s[p1, p2, 
   g] + \[Mu]21s[p1, p2]; \[Eta]1s[p1_, p2_, g_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11s[p2, g] + p2*y2s\), \(H*y2s\)], 
      1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); \[Mu]1s[p1_, 
  p2_] = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11s[p2, g] + p2*y2s\), \(H*y2s\)], 
     1]\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
p1r = {3}
p2r = {4}
gr = {7}
Q3r = N[ParallelTable[\[Mu]1q[p1r, p2r, gr]*\[Mu]11q[p1r, 
      p2r] + \[Eta]1q[p1r, p2r, gr]*\[Mu]21q[p1r, p2r] + \[Mu]1q[p1r, 
      p2r, gr]*\[Eta]11q[p1r, p2r, gr] + \[Eta]1q[p1r, p2r, 
      gr]*\[Eta]21q[p1r, p2r, gr] + \[Eta]1q[p1r, p2r, 
      gr]*(1 - \[Mu]21q[p1r, p2r] - \[Eta]21q[p1r, p2r, 
        gr]) + (1 - \[Mu]1q[p1r, p2r, gr] - \[Eta]1q[p1r, p2r, 
        gr])*\[Eta]01q[p2r, gr], {B, 3, 5}]]

Why do they get different results for {3,4,7}? The result in Programming 2 is what I want. I don't know why the result changes after adding another column.

POSTED BY: Shaoyan Robert
Rohit Namjoshi
Rohit Namjoshi
Posted 5 years ago

Compare

Table[x, {x, 2, 5}]
(* {2, 3, 4, 5} *)

and

Table[x, {x, 1/10, 3/10}]
(* {1/10} *)

The default increment for Table is 1. Specify the desired increment.

Table[x, {x, 1/10, 3/10, 1/10}]
(* {1/10, 1/5, 3/10} *)
POSTED BY: Rohit Namjoshi
Shaoyan Robert
Shaoyan Robert
Posted 5 years ago

Thank you, Namjoshi!
POSTED BY: Shaoyan Robert
Shaoyan Robert
Shaoyan Robert
Posted 5 years ago

Hi, Namjoshi One more question please. 

Clear["`*"];
L = 1; H = 2; \[Alpha] = 1/10;
\[Eta]1q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - y1q*\((p1 - H)\)\), \(H\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]01q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(p2\), \(H\)], 1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); y1q = \[Mu]11q + \[Eta]11q;
\[Eta]11q = \[Eta]21q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Mu]11q = \[Mu]21q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Mu]1q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - y1q*\((p1 - H)\)\), \(H\)], g]\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); \[Eta]1r = \[Eta]21r = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\); \[Eta]11s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Eta]21s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
\[Mu]21s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); y2s = \[Eta]21s + \[Mu]21s; \
\[Eta]1s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11s + p2*y2s\), \(H*y2s\)], 
      1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
       1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
      1\)] \[DifferentialD]x\)\); \[Mu]1s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11s + p2*y2s\), \(H*y2s\)], 1]\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
Q1 = Table[
   N[Maximize[{(p1 + p2)*\[Mu]1s*\[Eta]11s + 
       2*p2*\[Eta]1s*\[Eta]21s + (p2 + p1)*\[Eta]1s*\[Mu]21s, 
      H > L > 0 && 1 < g <= B && H >= p1 >= L && p2/g <= L && 
       g*p1 >= p2 >= p1}, {p1, p2, g}]], {B, 3, 5}];
Print["k72=", Q1]
Q2 = Table[
   N[Maximize[{2*p2*\[Eta]1r*\[Eta]21r, 
      H > L > 0 && B >= g > 1 && L <= p2 <= g*L}, {p2, g}]], {B, 3, 
    5}];
Print["k62=", Q2]
Q3 = Table[
   N[Maximize[{2*
        p1*\[Mu]1q*\[Mu]11q + (p1 + p2)*\[Eta]1q*\[Mu]21q + (p1 + 
          p2)*\[Mu]1q*\[Eta]11q + 2*p2*\[Eta]1q*\[Eta]21q + 
       p2*\[Eta]1q*(1 - \[Mu]21q - \[Eta]21q) + 
       p2*(1 - \[Mu]1q - \[Eta]1q)*\[Eta]01q, 
      H > L > 0 && 1 < g <= B && p1 <= p2 && 
       2*p1 <= p2 <= g*p1 <= g*H && H >= p1 >= L && p2/g <= L}, {p1, 
      p2, g}]], {B, 3, 5}];
Print["k52=", Q3]
q = N[{Q1, Q2, Q3}]
q3 = Transpose[{Q1, Q2, Q3}];
cycg = MaximalBy[#, First] & /@ q3;
cycg2 = MinimalBy[#, Last] & /@ cycg
cycg2[[All, All, 1]]
ListLinePlot[cycg2[[All, 1, 1]], DataRange -> {3, 5}, 
 PlotLegends -> {"\[Pi]"}]
ListLinePlot[Flatten[cycg2[[All, All, 2, 1, 2]]], DataRange -> {3, 5},
  PlotLegends -> {"p1"}]
ListLinePlot[Flatten[cycg2[[All, All, 2, 2, 2]]], DataRange -> {3, 5},
  PlotLegends -> {"p2"}]
ListLinePlot[Flatten[cycg2[[All, All, 2, 3, 2]]], DataRange -> {3, 5},
  PlotLegends -> {"g"}]

Above code runs well, but I also want to use the optimal result (i.e., the optimal combination of p1, p2 and g) to calculate Q3r = \[Mu]1q*\[Mu]11q + \[Eta]1q*\[Mu]21q + \[Mu]1q*\[Eta]11q + \ \[Eta]1q*\[Eta]21q + \[Eta]1q*(1 - \[Mu]21q - \[Eta]21q) + (1 - \ \[Mu]1q - \[Eta]1q)*\[Eta]01q Actually, this is a part of Q3. The difficulty lies in that we have to incoporate the the optimal combination of p1, p2 and g into \[Mu]1q, \[Mu]11q, etc. to derive their values.
Could you please tell me how to realize it? Thank you very much!
POSTED BY: Shaoyan Robert
Shaoyan Robert
Shaoyan Robert
Posted 5 years ago

A similar example but more simple.

Clear["`*"];
Maximize[{x - 2 y, x^2 + y^2 <= 1}, {x, y}]

If I want to use the optimal combination of x and y to calculate x-y, I can do it as follows:

Z = Maximize[{x - 2 y, x^2 + y^2 <= 1}, {x, y}]
x1 = Z[[2, 1, 2]]
y1 = Z[[2, 2, 2]]
x1 - y1

This is very easy to realize, but my above question is more difficult.
POSTED BY: Shaoyan Robert
Rohit Namjoshi
Rohit Namjoshi
Posted 5 years ago

There is at least one problem. There is a ; missing at the end of the Q = N[...] line. After fixing that, try calling the function for a specific B and ? to make sure it returns the value you expect. Then build the Table.
POSTED BY: Rohit Namjoshi
Shaoyan Robert
Shaoyan Robert
Posted 5 years ago

Thank you, Namjoshi. It works now. I use the code Table[{B, \[Alpha], f[B, \[Alpha]]}, {B, 2, 5}, {\[Alpha], 1/10, 3/10}]. The output is 

{{{2, 1/10, {{2.52632, {p1 -> 1., p2 -> 1.52632, 
      g -> 4.}}, {2.52632, {p1 -> 1., p2 -> 1.52632, 
      g -> 1.75}}}}}, {{3, 1/
   10, {{3.05263, {p1 -> 1., p2 -> 2.05263, 
      g -> 4.}}, {3.05263, {p1 -> 1., p2 -> 2.05263, 
      g -> 2.5}}}}}, {{4, 1/
   10, {{3.57895, {p1 -> 1., p2 -> 2.57895, 
      g -> 8.}}, {3.57895, {p1 -> 1., p2 -> 2.57895, 
      g -> 3.25}}}}}, {{5, 1/
   10, {{4.10526, {p1 -> 1., p2 -> 3.10526, 
      g -> 8.}}, {4.10526, {p1 -> 1., p2 -> 3.10526, g -> 4.}}}}}}

But why there is no output of B=2, alpha=3/10 (or 2/10)?
POSTED BY: Shaoyan Robert
Rohit Namjoshi
Rohit Namjoshi
Posted 5 years ago

Have you tried wrapping the code in a function with B and ? as parameters?

Clear["`*"];
L = 1; H = 3;
f[B_, ?_] := Module[{},
 (* The code from above *)
 ]

and then calling it for different values of B and ??

f[2, 1/10]

Rather than printing the result, the last expression should be MaximalBy[Q, First]. Then you can build a table of the result for different B and ?.

Table[{B, ?, f[B, ?]}, {B, 2, 10}, {?, 0.1, 0.95, .05}]
POSTED BY: Rohit Namjoshi
Shaoyan Robert
Shaoyan Robert
Posted 5 years ago

Thank you, Namjoshi. It seems that Table[{B, ?, f[B, ?]}, {B, 2, 10}, {?, 0.1, 0.95, .05}] doesn't work well.
POSTED BY: Shaoyan Robert
Rohit Namjoshi
Rohit Namjoshi
Posted 5 years ago

Can you be more specific? What do you mean by "doesn't work well"?
POSTED BY: Rohit Namjoshi
Shaoyan Robert
Shaoyan Robert
Posted 5 years ago

According to your suggestion, the code is:

Clear["`*"];
H = 13/10; L = 1; 
f[B_, \[Alpha]_] := Module[{}, \[Eta]1a = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - \((p1 - L)\)\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\)); \[Eta]2a = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(p2\), \(H\)], 1], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(p2\), \(L\)], 1], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\)); \[Eta]3a = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[Max[
\*FractionBox[\(H*\[Eta]2a - p1*\[Eta]2a + p2\), \(H\)], 1], B]\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[Max[
\*FractionBox[\(L*\[Eta]2a - p1*\[Eta]2a + p2\), \(L\)], 1], B]\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\)); \[Eta]1b = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - L)\)\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\)) + (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\)); \[Eta]2b = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(p2\), \(H\)], 1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(p2\), \(L\)], 1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\)); \[Eta]3b = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[Max[
\*FractionBox[\(H*\[Eta]2b - p1*\[Eta]2b + p2\), \(H\)], 1], g]\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[Max[
\*FractionBox[\(L*\[Eta]2b - p1*\[Eta]2b + p2\), \(L\)], 1], g]\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\)); \[Eta]11c = \[Eta]21c = \
\[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\); \[Mu]11c = \[Mu]21c = \[Alpha]*\
\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Eta]1c = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], 1], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(p2\), \(L\)], 1], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Mu]1c = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Eta]01d = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(p2\), \(H\)], 1], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
  \[Eta]11d = \[Eta]21d = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
  \[Mu]11d = \[Mu]21d = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); 
  y1d = \[Mu]11d + \[Eta]11d; \[Eta]1d = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - y1d*\((p1 - H)\)\), \(H\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Mu]1d = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - y1d*\((p1 - H)\)\), \(H\)], B]\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Eta]1f = \[Eta]21f = \
\[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[1, 
\*FractionBox[\(p2\), \(H\)]], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[1, 
\*FractionBox[\(p2\), \(L\)]], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\); \[Eta]11h = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[1, 
\*FractionBox[\(p2\), \(H\)]], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[1, 
\*FractionBox[\(p2\), \(L\)]], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Eta]21h = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Mu]21h = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], B]\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); 
  y2h = \[Eta]21h + \[Mu]21h; \[Mu]1h = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11h + p2*y2h\), \(H*y2h\)], 1], 
       B]\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Eta]1h = \[Alpha]*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11h + p2*y2h\), \(H*y2h\)], 1], 
         B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\)) + (1 - \[Alpha])*(\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], B]\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\)); \[Eta]11j = \[Eta]21j = \
\[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\); \[Mu]11j = \[Mu]21j = \[Alpha]*\
\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Eta]1j = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Mu]1j = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Eta]1k = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - y1k*\((p1 - H)\)\), \(H\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
  \[Eta]01k = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(p2\), \(H\)], 1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); 
  y1k = \[Mu]11k + \[Eta]11k;
  \[Eta]11k = \[Eta]21k = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\); \[Mu]11k = \[Mu]21k = \[Alpha]*\
\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Mu]1k = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - y1k*\((p1 - H)\)\), \(H\)], g]\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Eta]1m = \[Eta]21m = \
\[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\); \[Eta]11O = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
  \[Eta]21O = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
  \[Mu]21O = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); 
  y2O = \[Eta]21O + \[Mu]21O; \[Eta]1O = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11O + p2*y2O\), \(H*y2O\)], 
        1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Mu]1O = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11O + p2*y2O\), \(H*y2O\)], 1]\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Eta]11P = \[Eta]21P = \[Alpha]*\
\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Mu]11P = \[Mu]21P = \
\[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Eta]1P = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Mu]1P = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Eta]1q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2 - y1q*\((p1 - H)\)\), \(H\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
  \[Eta]01q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(p2\), \(H\)], 1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); 
  y1q = \[Mu]11q + \[Eta]11q;
  \[Eta]11q = \[Eta]21q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Mu]11q = \[Mu]21q = \
\[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Mu]1q = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Min[
\*FractionBox[\(p2 - y1q*\((p1 - H)\)\), \(H\)], g]\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Eta]1r = \[Eta]21r = \
\[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
          1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2\), \(L\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\); \[Eta]11s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[1, 
\*FractionBox[\(p2\), \(H\)]]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
  \[Eta]21s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)], \(g\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
  \[Mu]21s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), 
FractionBox[\(p2 - \((p1 - H)\)\), \(H\)]]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\); 
  y2s = \[Eta]21s + \[Mu]21s; \[Eta]1s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11s + p2*y2s\), \(H*y2s\)], 
        1]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 
         1\)] \[DifferentialD]x\)\) + (1 - \[Alpha])*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Min[
\*FractionBox[\(p2\), \(L\)], g]\), \(g\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(g\), \(B\)]\(
\*FractionBox[\(1\), \(B - 
        1\)] \[DifferentialD]x\)\); \[Mu]1s = \[Alpha]*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(1\), \(Max[
\*FractionBox[\(\((H - p1)\)*\[Eta]11s + p2*y2s\), \(H*y2s\)], 1]\)]\(
\*FractionBox[\(1\), \(B - 1\)] \[DifferentialD]x\)\);
  k72 = Maximize[{(p1 + p2)*\[Mu]1s*\[Eta]11s + 
      2*p2*\[Eta]1s*\[Eta]21s + (p2 + p1)*\[Eta]1s*\[Mu]21s, 
     H > L > 0 && 1 < g <= B && H >= p1 >= L && p2/g <= L && 
      g*p1 >= p2 >= p1}, {p1, p2, g}];
  k62 = Maximize[{2*p2*\[Eta]1r*\[Eta]21r, 
     H > L > 0 && B >= g > 1 && L <= p2 <= g*L}, {p2, g}];
  k52 = Maximize[{2*
       p1*\[Mu]1q*\[Mu]11q + (p1 + p2)*\[Eta]1q*\[Mu]21q + (p1 + 
         p2)*\[Mu]1q*\[Eta]11q + 2*p2*\[Eta]1q*\[Eta]21q + 
      p2*\[Eta]1q*(1 - \[Mu]21q - \[Eta]21q) + 
      p2*(1 - \[Mu]1q - \[Eta]1q)*\[Eta]01q, 
     H > L > 0 && 1 < g <= B && p1 <= p2 && 
      2*p1 <= p2 <= g*p1 <= g*H && H >= p1 >= L && p2/g <= L}, {p1, 
     p2, g}];
  k42 = Maximize[{2*
       p1*\[Mu]1P*\[Mu]11P + (p1 + p2)*\[Eta]1P*\[Mu]21P + (p1 + 
         p2)*\[Mu]1P*\[Eta]11P + 2*p2*\[Eta]1P*\[Eta]21P, 
     H > L > 0 && 1 < g <= B && p1 <= p2 <= 2*p1 && H >= p1 >= L && 
      p2/g <= L}, {p1, p2, g}];
  k7 = Maximize[{(p1 + p2)*\[Mu]1O*\[Eta]11O + 
      2*p2*\[Eta]1O*\[Eta]21O + (p2 + p1)*\[Eta]1O*\[Mu]21O, 
     H > L > 0 && 1 < g <= B && H >= p1 >= L && L <= p2/g <= H && 
      g*p1 >= p2 >= p1}, {p1, p2, g}];
  k6 = Maximize[{2*p2*\[Eta]1m*\[Eta]21m, 
     H > L > 0 && B >= g > 1 && L <= p2/g <= H}, {p2, g}];
  k5 = Maximize[{2*
       p1*\[Mu]1k*\[Mu]11k + (p1 + p2)*\[Eta]1k*\[Mu]21k + (p1 + 
         p2)*\[Mu]1k*\[Eta]11k + 2*p2*\[Eta]1k*\[Eta]21k + 
      p2*\[Eta]1k*(1 - \[Mu]21k - \[Eta]21k) + 
      p2*(1 - \[Mu]1k - \[Eta]1k)*\[Eta]01k, 
     H > L > 0 && 1 < g <= B && p1 <= p2 && 
      2*p1 <= p2 <= g*p1 <= g*H && H >= p1 >= L && 
      L <= p2/g <= H}, {p1, p2, g}];
  k4 = Maximize[{2*
       p1*\[Mu]1j*\[Mu]11j + (p1 + p2)*\[Eta]1j*\[Mu]21j + (p1 + 
         p2)*\[Mu]1j*\[Eta]11j + 2*p2*\[Eta]1j*\[Eta]21j, 
     H > L > 0 && 1 < g <= B && p1 <= p2 <= 2*p1 && H >= p1 >= L && 
      L <= p2/g <= H}, {p1, p2, g}];
  y7 = Maximize[{(p1 + p2)*\[Mu]1h*\[Eta]11h + 
      2*p2*\[Eta]1h*\[Eta]21h + (p2 + p1)*\[Eta]1h*\[Mu]21h, 
     H > L > 0 && g >= B > 1 && p1 <= p2 < g*p1 <= g*H && 
      L <= p1 <= H && p2 <= B*H}, {p1, p2, g}];
  y6 = Maximize[{2*p2*\[Eta]1f*\[Eta]21f, 
     H > L > 0 && g >= B > 1 && L <= p2 <= B*H}, {p2, g}];
  y5 = Maximize[{2*
       p1*\[Mu]1d*\[Mu]11d + (p1 + p2)*\[Eta]1d*\[Mu]21d + (p1 + 
         p2)*\[Mu]1d*\[Eta]11d + 2*p2*\[Eta]1d*\[Eta]21d + 
      p2*\[Eta]1d*(1 - \[Mu]21d - \[Eta]21d) + 
      p2*(1 - \[Mu]1d - \[Eta]1d)*\[Eta]01d, 
     H > L > 0 && g >= B > 1 && p1 <= p2 && 
      2*p1 <= p2 <= g*p1 <= g*H && H >= p1 >= L}, {p1, p2, g}];
  y4 = Maximize[{2*
       p1*\[Mu]1c*\[Mu]11c + (p1 + p2)*\[Eta]1c*\[Mu]21c + (p1 + 
         p2)*\[Mu]1c*\[Eta]11c + 2*p2*\[Eta]1c*\[Eta]21c, 
     H > L > 0 && g >= B > 1 && p1 <= p2 <= 2*p1 && 
      H >= p1 >= L}, {p1, p2, g}];
  k1 = Maximize[{2*p1*(1 - \[Eta]1b)^2 + 
      2*(p1 + p2)*\[Eta]1b*(1 - \[Eta]1b) + 2*p2*(\[Eta]1b)^2, 
     H > L > 0 && 1 < g <= B && 0 < p1 <= L && g*p1 >= p2 >= p1}, {p1,
      p2, g}];
  k2 = Maximize[{2*p2*(\[Eta]2b)^2, 
     H > L > 0 && 1 < g <= B && 0 < p2 <= B*H && p2 <= g*L}, {p2, g}];
  k3 = Maximize[{(p1 + p2)*\[Eta]3b*\[Eta]2b + 
      2*p2*(1 - \[Eta]3b)*\[Eta]1b + (p2 + 
         p1)*(1 - \[Eta]3b)*(1 - \[Eta]1b), 
     H > L > 0 && 1 < g <= B && 0 < p1 <= L && g*p1 >= p2 >= p1}, {p1,
      p2, g}];
  y1 = Maximize[{2*p1*(1 - \[Eta]1a)^2 + 
      2*(p1 + p2)*\[Eta]1a*(1 - \[Eta]1a) + 2*p2*(\[Eta]1a)^2, 
     H > L > 0 && g >= B > 1 && 0 < p1 <= L && g*p1 >= p2 >= p1}, {p1,
      p2, g}];
  y2 = Maximize[{2*p2*(\[Eta]2a)^2, 
     H > L > 0 && g >= B > 1 && 0 < p2 <= B*H && p2 <= g*L}, {p2, g}];
  y3 = Maximize[{(p1 + p2)*\[Eta]3a*\[Eta]2a + 
      2*p2*(1 - \[Eta]3a)*\[Eta]1a + (p2 + 
         p1)*(1 - \[Eta]3a)*(1 - \[Eta]1a), 
     H > L > 0 && g >= B > 1 && 0 < p1 <= L && g*p1 >= p2 >= p1}, {p1,
      p2, g}];
  Q = N[{y1, y2, y3, k1, k2, k3, y4, y5, y6, y7, k4, k5, k6, k7, k42, 
      k52, k62, k72}]
    MaximalBy[Q, First]]
Table[{B, \[Alpha], f[B, \[Alpha]]}, {B, 2, 4}, {\[Alpha], 1/10, 3/10,
   1/10}]

I encounter some problems when I ran it.
POSTED BY: Shaoyan Robert
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