Assuming I didn't make any stupid mistakes:
- NIntegrate -> Integrate, evaluate by itself first, get analytic expression
- replace z with Min expression in there
- replace last condition with y<=x, x<=1 (0<=y is covered by the one containing b for the given values)
Then I end up with:
In[11]:= Table[
NMaximize[{(b x)/2 - 0.375` b x^2 + 0.375` b x y - (b y^2)/2 -
0.125` b x Min[1, 1.4285714285714286` (x - 0.3` y)] +
0.125` b y Min[1, 1.4285714285714286` (x - 0.3` y)],
b*(1 - y) <= 1, y <= x, x <= 1}, {x, y}], {b, 1., 1.5, 0.1}]
Out[11]= {{0.161458, {x -> 0.645833,
y -> 0.354167}}, {0.177604, {x -> 0.645833,
y -> 0.354167}}, {0.19375, {x -> 0.645833,
y -> 0.354167}}, {0.209896, {x -> 0.645833,
y -> 0.354167}}, {0.226042, {x -> 0.645833,
y -> 0.354167}}, {0.242187, {x -> 0.645833, y -> 0.354167}}}
Hope this helps,
Peter
