D,E

Hart Manwlacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor hour requirements, by drpartment, are as felows. During the next prosuction period, the labor-hours waibtie are 450 in departrint A, aso in department B, and so in department C. The prekt contributions per unit are s25 for product 3 , saz for product 2 , and s2e for product 3 . (a) Fermulate a Inese proganming model for maximiting total prefit contribution. (Let pj= units of product i produced, for i =1,2,3.) Department 8 Departinent c P1,P2,P30 (b) Solve the Inaar program formulated in part (o). How much of each product should be preduced, and what ia the profected tocal profe contribution (hn dollamy? (P1,P2,P3)=()withprehto (c) Arer evaluating the solvtion obtained in part (b), one of the production supervisors noted that production setup coste had not been taken into account. she noted uhat aetup costs arie fliog tor costs? (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)? (P12,P2,P3)=(1)withprofit5 (c) After evaluating the solution obtained in part (b), one of the produetion suptrvisors noted that preductica setup costs had not been taken into account. She noted that setup costs are slibe f product 1,$540 for product 2 , and $630 for product 2 . If the solution developed in part (b) is to be used, what is the total profit contribution (in dollars) after taking into account the setue costs? (d) Management realizes that the optimal product mix, taking setup costs into account, might be ditferent from the coe recomenended in part (b). Formulate a mixed-integer linear program that takes setup costs into account. Nanagement also itated that we should not censider making more than 145 units of product 1 , 150 units of product 2 , or 190 units of preduct 3 . (Let P, " unit of product i produced and yi be the 0.1 variable that is one if any quantity of product i is produced and zero echerwise, for i=1,2,3.) What is the objective function of the mixed-integer Inear program? In addition to the constraints from part (a), what other constrains should be asded to the mined integer linear program? s.t. units of Product 1 preduced units of Product 2 produced units of Product 3 produced p1,P2,P2+of1,2,3=0,1 (e) Solve the mised-integer linear peogram formulated in part ( ). How much of each podoct should be produced, and whet is the projected rotal profi (in dellars) contribution). (3,2,2,1,2,3)=( with peoft s