Question: Problem 1. Consider the optimization problem max 4z + 5z2 +423 + 8z4 +625 4z1 +672 + 5z3 +974 +725 0, j= 1, ...,5. Assume

Problem 1. Consider the optimization problem max 4z + 5z2 +423

Problem 1. Consider the optimization problem max 4z + 5z2 +423 + 8z4 +625 4z1 +672 + 5z3 +974 +725 0, j= 1, ...,5. Assume that all zj may take only nonnegative integer values. (a) Formulate a dynamic programming problem for solving problem (1). Describe the state space, the action space, the feasible action mapping, and the dynamic programming equation. (b) Use the dynamic programming equations to obtain the optimal solution. For all problems, you can use any software to code the dynamic programming equation and solve. However, you cannot use an optimization solver to solve the problems. Please, provide printouts. Problem 1. Consider the optimization problem max 4z + 5z2 +423 + 8z4 +625 4z1 +672 + 5z3 +974 +725 0, j= 1, ...,5. Assume that all zj may take only nonnegative integer values. (a) Formulate a dynamic programming problem for solving problem (1). Describe the state space, the action space, the feasible action mapping, and the dynamic programming equation. (b) Use the dynamic programming equations to obtain the optimal solution. For all problems, you can use any software to code the dynamic programming equation and solve. However, you cannot use an optimization solver to solve the problems. Please, provide printouts

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