Question 1: Optimization in Resources/Inventory/Production Management. (20 Marks) A used car dealer has three used cars to allocate to three showrooms in three different cities. The estimated expected profits from used car sales (in AED thousands) for each showroom are in the following table. Number of used cars Profits (AED 1000) Showroom 1 Showroom 2 Showroom 3 0 0 0 0 4 7 5 2 10 8 8 12 11 11 The dealer's objective is to find the best allocation of used cars to the showrooms in order to maximize his total profit. 1. Formulate this problem into a deterministic dynamic programming model, by defining: a. The stages and their number. b. The decision variables and the relation between them. c. The states, and the value of at stage n, n= 1,2,3. d. The profit of allocating used cars to showroom i. e. The objective function and its maximum. 2. Solve the problem by constructing the tables for , , and. (11 Marks) 3. Based on the tables you constructed write down the optimal allocation, and the maximum total profit. (5 Marks) 4. Interpret the solution in terms of the dealer's objective. (1.5 Marks) Question 1: Optimization in Resources/Inventory/Production Management. (20 Marks) A used car dealer has three used cars to allocate to three showrooms in three different cities. The estimated expected profits from used car sales (in AED thousands) for each showroom are in the following table. Number of used cars Profits (AED 1000) Showroom 1 Showroom 2 Showroom 3 0 0 0 0 4 7 5 2 10 8 8 12 11 11 The dealer's objective is to find the best allocation of used cars to the showrooms in order to maximize his total profit. 1. Formulate this problem into a deterministic dynamic programming model, by defining: a. The stages and their number. b. The decision variables and the relation between them. c. The states, and the value of at stage n, n= 1,2,3. d. The profit of allocating used cars to showroom i. e. The objective function and its maximum. 2. Solve the problem by constructing the tables for , , and. (11 Marks) 3. Based on the tables you constructed write down the optimal allocation, and the maximum total profit. (5 Marks) 4. Interpret the solution in terms of the dealer's objective. (1.5 Marks)