Question

Problem #5: A plant can manufacture five products P1, P2, P3, P, and Ps. The plant consists of two work areas: the job shop area A, and the assembly area Az. The time required to process one unit of product P, in work area A, is Pu (in hours). for i = 1, 2 and j = 1,...,5. The weekly capacity of work area A, is in hours). The company can sell all it produces of product P, at a profit of ;, for j = 1,...,5. The plant manager thought of writing a linear program to maximize profits, but never actually did for the following reason: From past experience, he observed that the plant operates'best when at most two products are manufactured at a time. lle believes that if he uses linear programming, the optimal solution will consist of producing all five products. Do you agree with him? Explain, based on your knowledge of linear programming,

Answer 1

cenifs 4 two w to the number of constiaint, 80 Given that :- #plant con manufacture fise peoduela. in P, P2, P3, Pu 4 Ps. The plant consists of two wouk ahed: the job oshop' area t, and the assembly Area 9. the Lime requised to process are unit Pj in mouk leed Ai is Pi for i=1,2 and the weekly copacity of cusuk area Ay is G This Lp model consists of an objective function To marimize the profit and tuto constraints Weekly production hawis at each curea The variable lace how many of each Pr, P2, P3, P4 & P, to Peroduce Max P, S, + P₂ Sqf P₂ S₃ f Pq Su t Ps S5 "CP; + Pat Pat Put Ps) ti sa .(P + P ₂7 P ₂ + Py+Ps) to see and P, P2, P3 , Py and Ps >o $ 4 modul always has an o fimal, basic gsolution In such qolutions, there will always be a as long as it is feasible and bonded. Feaed number g Basic uoviables which be geecalar than zew. The cust will be non basic and hence at most luo uouickles may be gevate them zun- Hence the oflimum solution will ocul only tohen at most trus duodecte care produced at a time. Subject to CA