PLEASE USE EXCEL

1. (100 points) Yorktown manufacturing makes three products. Each product requires manufacturing op- erations in three departments: X, Y, and Z. The labour hour requirements, by department, are as follows: Department X Product 1 Product 2 Product 3 1.50 3.00 2.00 Y 2.00 1.00 2.50 Z 0.25 0.25 0.25 During the next production period, the labor-hours available are 465 in department X, 345 in department Y, and 50 in department Z. The profit contributions per unit are $30 for product 1, $25 for product 2, and $35 for product 3. 1. Formulate a linear programming model for maximizing total profit contribution. 2. Solve the linear program formulated in part (1). How much of each product should be produced and what is the projected total profit contribution? (make sure that the number of products are integer valued). 3. After evaluating the solution in part (2), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $400 for product 1, $550 for product 2, and $600 for product 3. If the solution developed in part (2) is to be used, what is the total profit contribution after taking into account the setup costs? 4. Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (2). Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 175 units of product 1, 150 units of product 2, or 140 units of product 3. 5. Solve the mixed-integer linear program formulated in part (4). How much of each product should be produced, and what is the projected total profit contribution? compare this profit contribution to that obtained in part (3). (make sure that the number of products are integer valued)