Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows: Department A B Product 1 1.50 2.00 Product 2 3.00 1.00 Product 3 2.00 2.50 C 0.25 0.25 0.25 During the next production period the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $25 for product 1, $28 for product 2, and $30 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution. If the constant is "1" it must be entered in the box. If required, round your answers to two decimal places. Let Pi units of product i produced Max $ P1 + $ P2 + $ P3 s.t. P1 + P2 + P3 - Select your answer - P1 + P2 + P3 - Select your answer P1 + P2 + P3 - Select your answer- P1, P2, P3 O (b) Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution? Amount to Produce Product 1 Product 2 Product 3 Profit $ (c) After evaluating the solution obtained in part (b), 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 (b) is to be used, what is the total profit contribution after taking into account the setup costs? $