Consider the following problem:

Maximize Z= 3x_1^2 - x_1^3 + 5x_2^2 - x_2^3, subject to x_1 + 2x_2 less than or equal to 4 X_1, X_2 greater than or equal to 0 x_1, x_2 are integers Solve this problem by dynamic programming. Specify stages, states, decision variables, the value function, its reclusive relationship and show the intermediate steps of the solution procedure. Identify the optimal solution and the optimal objective value. Maximize Z= 3x_1^2 - x_1^3 + 5x_2^2 - x_2^3, subject to x_1 + 2x_2 less than or equal to 4 X_1, X_2 greater than or equal to 0 x_1, x_2 are integers Solve this problem by dynamic programming. Specify stages, states, decision variables, the value function, its reclusive relationship and show the intermediate steps of the solution procedure. Identify the optimal solution and the optimal objective value