A plant can manufacture five products P1 , P2 , P3 , P4 , and P5 . The
plant consists of two work areas: the job shop area A1 and the assembly area A2 .
The time required to process one unit of product P j in work area A i is pi j (in
hours), for i = 1, 2 and j = 1, . . . , 5. The weekly capacity of work area A i is C i
(in hours). The company can sell all it produces of product P j at a profit of s j , for
i = 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. He
believes that if he uses linear programming, the optimal solution will consist of
producing all five products and therefore it will not be of much use to him. Do you
agree with him? Explain, based on your knowledge of linear programming.
