(C) This problem considers maxima of functions f : C > R where f is a convex function and G g R\" is a convex set. (i) Assume f is a not the constant function over C. Show that f does not attain a maximum at any point in the int(C). (ii) Assume C is a compact convex set and that f is continuous and convex over C. Show that at least one maximizer is an extreme point of C. (Hint: Assume statement is false and prove a contradiction.)