3. [30 points] Consider the following integer nonlinear programming problem. Maximize Z = 32x1 - 2x} + 30x2 + 20xz subject to 3x + 7x2 + 5x3 = 20 and X1, X2, Xz are nonnegative integers. Use dynamic programming to solve this problem. Backward Formulation Stage (n): Sub-index of variable xn (n = 1,2,3) o State (Sn): Amount of slack remaining in the constraint at stage n Decision Variable (Xn): Value of variable xn (n = 1, 2, 3) Let Pn(X) be p.(x1) = 32x2 2x, P2(x2) = 30x2, and P3 (x3) = 20xz. o Return Function (fn (sn, xn)): In(sm,xn) = Pn(x) + fr+1(Sn+1) Recursive Relation (fi (sn)): fi (sn) = max{pn(xn) + fi+1(Sn+1)} Xn (a) (5 points) Complete the table in Stage 3. Stage 3 Subproblem at Stage 3 Maximize 20x3 subject to 5x3 553 and xz is a nonnegative integer. S3 f3(83) x3 0 20 0 1 0-4 5-9 10-14 15-19 20 Stage 2 Subproblem at Stage 2 Maximize 30x2 subject to 7x2