Question: (a) Consider the problem of maximizing \(f\left( x \right)\) subject to \(g\left( x \right)+\alpha \le 0\), where \(x\in D\subset {{R}^{n}}\) and \(\alpha \in A\subset R\). Suppose that \(f\) is concave and \(g\) is convex, \(D\) is open and convex, and A is convex. Assuming that the solution to problem exists, prove that the maximum value function \(F\left( \alpha \right)=f\left( x\left( \alpha \right) \right)\) is concave

(b) Solve the problem of maximizing \(10x-{{x}^{2}}\) subject to \(\alpha -x\ge 0\), for \(\alpha \in R\), and determine the maximum value function

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