First of all, I am sorry for the title but I do not know what I am actually looking for.
I have the following three equations: $$ A = \frac{1}{x}\\ B = \frac{s + 1}{4}\\ C = \frac{s}{x} + \frac{1-s}{4} $$ And I know that: $$ 2 < x \leq 4\\ 0 \leq s \leq 1 $$ And I want to maximize the following function: $$ \min(A, B) - C = \min(\frac{1}{x}, \frac{s+1}{4}) - \frac{s}{x} - \frac{1-s}{4} $$
All I have basically figured out is that his is in fact not a lineair optimization (because of the $\frac{s}{x}$ term). How do I solve this?
You have $$\min(\frac{1}{x},\frac{s+1}{4})-\frac{2}{x}-\frac{1-s}{4}$$ with $$2<x\le 4$$ and $$0\le s\le 1$$ For $$\frac{1}{x}\geq \frac{s+1}{4}$$ you have to maximize $$f(x,s)=\frac{s+1}{4}-\frac{s}{x}-\frac{1-s}{4}$$ and i have got $$(\frac{1}{16};s=\frac{1}{2},x=\frac{8}{3})$$ in the other case $$f(x,s)=\frac{1}{x}-\frac{s}{x}-\frac{1-s}{4}$$ and here i have got $$(\frac{1}{16};x=\frac{8}{3},s=\frac{1}{2})$$