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For 0<x<1 and 0<y<1, the function needs to satisfy the following:

f(x,y) < 0 for x<0.5 and/or y<0.5

f(x,y) = 0 for x=0.5 and y=0.5

f(x,y) > 0 for x>0.5 and y>0.5

MUST be concave.. i.e. second order partials wrt X and Y must both be < 0.

My maths was never that good and I can't seem to make any progress here.. can anyone help out? Thanks