5. [10 pts] Consider the following maximization problem: max f(3:, k) = 2163: 9:2 {E (a) Find the optimal value for a: that maximizes f (33,16) = 2163: m2. Treat "k" as a constant. Verify that the second order condition is satised. (b) Is this f(:c,k) linear in "k"? Let F(k) = f(:1:(k),k) denote the function of "k" obtained by inserting the optimal value for so into the function f (22,16). Find this function FUc) and show that FUc) is convex in k