The Wearever 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.
a. Formulate a goal programming model to determine the amount of shag and sculptured carpet to produce to best meet the company’s goals.
b. Solve this model by using the computer.