Problem 1. (25 points) G-star Company is considering three products. The manager needs to decide which products to produce and the production quantities. Product 1 and Product 2 will need a set up cost to start the production. For each product, the production of one unit will have a cost and use a proportion of the production capacity. For each product, each unit sold will generate a revenue. Product Set up cost Cost per unit Revenue per unit Capacity used per unit, % 20 The demand for Product 1 is up to 3 units. As for the other two products, all units produced could be sold. The objective is to maximize the total profit. (a) If the production quantities for the three products must be integers, use dynamic pro- gramming to solve this problem. Please list all of the optimal production plans. (b) If the production quantities for the three products can be fractional, use dynamic pro- gramming to solve this problem. Please list all of the optimal production plans. Problem 1. (25 points) G-star Company is considering three products. The manager needs to decide which products to produce and the production quantities. Product 1 and Product 2 will need a set up cost to start the production. For each product, the production of one unit will have a cost and use a proportion of the production capacity. For each product, each unit sold will generate a revenue. Product Set up cost Cost per unit Revenue per unit Capacity used per unit, % 20 The demand for Product 1 is up to 3 units. As for the other two products, all units produced could be sold. The objective is to maximize the total profit. (a) If the production quantities for the three products must be integers, use dynamic pro- gramming to solve this problem. Please list all of the optimal production plans. (b) If the production quantities for the three products can be fractional, use dynamic pro- gramming to solve this problem. Please list all of the optimal production plans