step by step solution

Hort Manufacturing makes three product. 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 avadabie are 450 in department A,350 in department B, and 50 in department C. The profit: contributions per unit are $27, for product 1,$29 for product 2, and $32 for product 3. (a) Formulate a linear programming model for maximcing total profit contribution, (Let P/= units of product i produced, for i=1,2,3) c) After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken inte account. She noted that setup costs are $390 for product 1,$560 for product 2 , and $650 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 165 units of product 1,175 units of product 2 , or 185 units of product 3. (Let 7= units of product 1 produced and y be the 01 varable that is one if any quantity of product ( is produced and zero otherwise, for i=1,2,3. What is the objective function of the mixedinteger linear program? Max In addition to the constraints from part (s), what other constraints should be added to the mixed-integer linear prooram? s.t. units of Product 1 produced units of ProdOct 2 produced units of Product a produced 1,P2,P3=0;y1,Y2,Y3=0,1 (e) Solve the mixed-integer linear program formulated in part (d). How much of each preduct should be produced, and what is the projected total profit (in dollars) contribution? (P1,P2,P3,y1,Y2,y2)=(withprofit: