3. (a) Consider the following nonlinear programming problem. Maximize Z = 4x + x + 2x} +12 subject to 3x1 + 2x2 + x3 = 9 x1 2 0,x2 > 0,X3 20 Use dynamic programming to solve this problem. (b) Consider the following nonlinear programming problem. Maximize 2 = 36x +9x - 6x} +36x2 3x} subject to X1 + x2 0. Use dynamic programming to solve this problem. 3. (a) Consider the following nonlinear programming problem. Maximize Z = 4x + x + 2x} +12 subject to 3x1 + 2x2 + x3 = 9 x1 2 0,x2 > 0,X3 20 Use dynamic programming to solve this problem. (b) Consider the following nonlinear programming problem. Maximize 2 = 36x +9x - 6x} +36x2 3x} subject to X1 + x2 0. Use dynamic programming to solve this