Question: TheWearever 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 under-utilize production capacity, which is 480 hours.
(2) Achieve product demand of 40 lots for shag and 50 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.