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. 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,$27 for product 2 , and $29 for product 3 . (a) Formulate a linear programming model for maximizing total profit contribution. (Let pi= units of product i produced, for i=1,2,3. Max s.t. Department A Department B Department C p1,p2,p30 (b) Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution (in dollars)? (p1,p2,p3)=(withprofit$ (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 $380 for product 1,$500 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 (in dollars) after taking into account the setup costs? $ (d) Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 140 units of product 1,190 units of product 2 , or 200 units of product 3 . (Let pi= units of product i produced and yi be the 01 variable that is one if any quantity of product i is produced and zero otherwise, for i=1,2,3.) What is the objective function of the mixed-integer linear program? Max In addition to the constraints from part (a), what other constraints should be added to the mixed-integer linear program? s.t. units of Product 1 produced units of Product 2 produced units of Product 3 produced p1,p2,p30;y1,y2,y3=0,1 (e) Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced, and what is the projected total profit (in dollars) contribution? (p1,p2p3y1y2,y3)=(