(4) (10 pts.) Let S = A = [0, 1]. Define f : S x A - R and y : A - 25 by f(x, a) = Va for (x, a) E S x A and y(a) = [0, va] for a E A. Let y* (a) be the set of maximizers of f (, a) on ya), and f*(a) = max{f (x, a)|x E y(a)}. (a) (5 pts.) Check if y*(a) is upper-hemicontinuous, compact-valued, or convex-valued. (b) (5 pts.) Check if f* (a) is a continuous function