Hi! I have tried to solve the following non-linear integer max-problem, without setting some lower (positive) bounds on Q1, Q2 & Q3, just being positive. Mathematica fails to find the optimal solotion, unless I increase the lower bounds for Q2 & Q3 to about 40. I have solved the same problem in LINGO and found the global solution {P -> 60., Q1 -> 0, Q2 -> 52., Q3 -> 60., y1 -> 0, y2 -> 1, y3 -> 1, \z1 -> 0, z2 -> 0, z3 -> 1} in less than a second. Any suggestions?
NMaximize[{(Q1 + Q2 + Q3) (P - 20) + 3*0.5 (80 - P) Q1*z1 +
2*0.5 (100 - 0.8 P) Q2*z2 + 2*0.5 (90 - 0.5 P) Q3*z3,
z1 + z2 + z3 == 1 && Q1 == (80 - P) y1 && Q2 == (100 - 0.8 P) y2 &&
Q3 == (90 - 0.5 P) y3 && 2 <= y1 + y2 + y3 <= 3 &&
3 <= y1 + y2 + y3 + z1 + z2 + z3 <= 4 &&
2 <= y1 + y2 + y3 + z1 <= 3 && 2 <= y1 + y2 + y3 + z2 <= 3 &&
2 <= y1 + y2 + y3 + z3 <= 3 && Q1 >= 0 && Q2 >= 0 && Q3 >= 0 &&
1 >= y1 >= 0 && 1 >= y2 >= 0 && 1 >= y3 >= 0 && z1 >= 0 &&
z2 >= 0 && z3 >= 0 && 80 > P > 20 && y1 \[Element] Integers &&
y2 \[Element] Integers && y3 \[Element] Integers &&
z1 \[Element] Integers && z2 \[Element] Integers &&
z3 \[Element] Integers}, {P, Q1, Q2, Q3, y1, y2, y3, z1, z2, z3}]
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