Consider the following code:

Table[NMaximize[{NIntegrate[(a*(1 - 0.25*z - (1 - 0.25)*x)*x + 
           a*(0.25*z - y + (1 - 0.25)*x)*y)/b, {a, 0, b}], 
       z = Min[1, (x - y*0.3)/(1 - 0.3)], b*(1 - y) <= 1, 
       0 <= y <= x <= 1}, {x, y}], {b, 1, 1.5, 0.1}]

I am trying to numerically solve an optimization problem (for x and y, for some b values). The problem has an integration in it. Interestingly, there is another variable z, which is a function of x and y, but cannot be greater than 1 (therefore I use Min function). Integration have issues because of the Min function. Any ideas?

Cheers, Ovunc