(a) Consider a convex set S CR and assume that for some c E R the maximization problem, max{c+x : x ES} (Q) has an optimal value 8. Then prove that the following statements are EQUI LENT: (S1) Let H = {r:0"x=}, then HNS contains at least two points. (S2) There exists an infinite number of optimal solutions to (Q). (S3) There exists an optimal solution to (Q) that is not an extreme point of S. (b) Consider the following constraints, X1 + 2x2 -X1 + 2x2