1. A furniture company manufactures two products, P1 and P2, through a two-fold operation: automatic (machine-assisted) processing and manual processing for finishing. The following gives the number of minutes required for each product.     Automatic Manual P1 16 20 P2 20 33   For the coming week, the company has 46 hours for the automatic operation and 42 hours for the manual operation. It was estimated that an hour of machine time costs $15 and finishing, $7. Any idle time in between is considered negligible. P1 and P2 are sold at $24 and $36 each, respectively. The company is obliged to produce 20 Pl's for a particular customer next week. Formulate the appropriate LP model to achieve optimal results in the coming week. Use x's for your decision variables.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter8: Evolutionary Solver: An Alternative Optimization Procedure
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1. A furniture company manufactures two products, P1 and P2, through a two-fold operation: automatic (machine-assisted) processing and manual processing for finishing. The following gives the number of minutes required for each product.
 
  Automatic Manual
P1 16 20
P2 20 33
 
For the coming week, the company has 46 hours for the automatic operation and 42 hours for the manual operation. It was estimated that an hour of machine time costs $15 and finishing, $7. Any idle time in between is considered negligible. P1 and P2 are sold at $24 and $36 each, respectively. The company is obliged to produce 20 Pl's for a particular customer next week. Formulate the appropriate LP model to achieve optimal results in the coming week. Use x's for your decision variables.
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