Formulate a goal programming model to determine the amount of shag and sculptured carpet to produce to best meet the company’s goals.

1. The Wear-ever Carpet Company manufactures two brands of carpet—shag and sculptured— in 100-yard lots. It requires 8 hours to produce one lot of shag carpet and 6 hours to produce one lot of sculptured carpet. The company has the following production goals, in prioritized order:

 

(1) Do not underutilize production capacity, which is 480 hours.

(2) Achieve product demand of 40 (100-yard) lots for shag and 50 (100-yard) lots for sculptured carpet. Meeting demand for shag is more important than meeting demand for sculptured, by a ratio of 5 to 2.

(3) Limit production overtime to 20 hours.

 

Formulate a goal programming model to determine the amount of shag and sculptured carpet

to produce to best meet the company’s goals.

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