I am a computer scientist, and find myself needing the following lemma:
If f(x)=(g(x))/(h(x)), where g and h are linear and positive with domain the convex polytope d, then extrema of f occur at vertices of d.
If that is not possible, the following would suffice:
If f(x)=(g(x))/(g(x)+h(x)), where g and h are linear and non-negative (and g + h is positive) with domain the convex polytope d, then extrema of f occur at vertices of d.
It seems that this is true. But I am having trouble proving it. Any help would be appreciated.