Solve the Following Question.

and p(2) > 0. 15. A fishery earns a profit of or (x) from catching and selling x units of fish. The firm owns a pool which currently has y, fish in it. If x e [0, yi ] fish are caught this period, the remaining i = y1-x fish will grow to f (i) fish by the beginning of the and next period, where f: R4 - R+ is the growth function for the fish population. mits The fishery wishes to set the volume of its catch in each of the next three periods offs so as to maximize the sum of its profits over this horizon. That is, it solves: Maximize m (x1) + (x2) + (x3) ctly subject to x1 _ yl if X2 5 12 = f()1 - x1) x3 - 13 = f(12 - x2) and the nonnegativity constraints that x 2 0, t = 1, 2, 3. Show that if it and f are continuous on R+, then the Weierstrass Theorem may be used to prove that a solution exists to this problem. (This is immediate if one can show that the continuity of f implies the compactness of the set of feasible triples (x1, X2, X3).)