A company produces two products (P1 and P2) using two machines (M/C1, M/C2). Following information is...

 

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A company produces two products (P1 and P2) using two machines (M/C1, M/C2). Following information is available: • Each machine works only one shift of 8 hours every day. • P1 has to be processed on both machines, i.e., it needs two processes: one on each machine. • If M/C1 is completely devoted to processing P1 only, then 24 units of P1 can be produced on M/C1 in a shift. • If M/C2 is completely devoted to processing P1 only, then 30 units of P1 can be produced on M/C2 in a shift. • P2 needs only one process. A unit of P2 can be processed on either of the machines. Any unit of P2 that is processed on M/C1 requires 15 minutes. Any unit of P2 that is processed on M/C2 requires 18 minutes. • Daily demands for P1 and P2 are at most 10 and 5, respectively. However, the demands can be increased by adver- tising. Each dollar spent advertising P1 increases its daily demand by 2 units, and each dollar spent advertising P2 increases its daily demand by 1 unit. • Due to marketing limitations, the number of P1 sold must be at least twice the number of P2 sold. • Unit sales profits (sales minus manufacturing costs) for P1 and P2 are $16 and $20, respectively. We would like to formulate an LP for the above problem considering total daily profits. (a) What type of problem, hence model is this? (b) Formulate the LP for the problem. A company produces two products (P1 and P2) using two machines (M/C1, M/C2). Following information is available: • Each machine works only one shift of 8 hours every day. • P1 has to be processed on both machines, i.e., it needs two processes: one on each machine. • If M/C1 is completely devoted to processing P1 only, then 24 units of P1 can be produced on M/C1 in a shift. • If M/C2 is completely devoted to processing P1 only, then 30 units of P1 can be produced on M/C2 in a shift. • P2 needs only one process. A unit of P2 can be processed on either of the machines. Any unit of P2 that is processed on M/C1 requires 15 minutes. Any unit of P2 that is processed on M/C2 requires 18 minutes. • Daily demands for P1 and P2 are at most 10 and 5, respectively. However, the demands can be increased by adver- tising. Each dollar spent advertising P1 increases its daily demand by 2 units, and each dollar spent advertising P2 increases its daily demand by 1 unit. • Due to marketing limitations, the number of P1 sold must be at least twice the number of P2 sold. • Unit sales profits (sales minus manufacturing costs) for P1 and P2 are $16 and $20, respectively. We would like to formulate an LP for the above problem considering total daily profits. (a) What type of problem, hence model is this? (b) Formulate the LP for the problem.

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