IGNORE THE FOLLOWING - IT ACTUALLY WORKED AFTER A SMALL CHEAT:)
This worked very well, thanks so much Peter!
Only issue, when the problem is bigger and also the integration bounds have "z" in them - it does not run at all.
oint3 = Integrate[(a*x*(1 - 0.25*z - (1 - 0.25)*x) +
a*y*(0.25*z - y + (1 - 0.25)*x))/b, {a, 0, 1/(1 - y)}] +
Integrate[(a*x*(1 - 0.25*z - (1 - 0.25)*x) +
y*(1 - a*(1 - 0.25*z - (1 - 0.25)*x)))/b, {a, 1/(1 - y),
1/(1 - (1 - 0.25)*x - 0.25*z)}] +
Integrate[x/b, {a, 1/(1 - (1 - 0.25)*x - 0.25*z), b}]
Let's say we maximize the sum of three integrals with the constraints
0 <= y <= x <= 1,
b*(1 - (1 - 0.25)*x - 0.25*Min[1, (x - y*0.1)/(1 - 0.1)]) >=
1}, {x, y}], {b, 1, 6, 0.1}]
The same idea just cannot be used. Any ideas?
I extremely appreciate your help in this.