A company manufactures two brands of carpet - Shag and sculptured in 100-yard lot. It requires 6 hours to produce one lot of shag carpet and 5 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 50 (100-yard) lots for shag and 50 (100-yard) lots for sculptured carpet. Meeting demand for shag carpet is more important than meeting demand for sculptured one, by a ratio of 3 to 2. (3) Limit production overtime to 20 hours if needed. Tasks: 1) Formulate a goal programming model to determine the amounts of shag and sculptured carpet to produce to best meet the company's goals. (5 marks) 2) Solve this model using the computer and give your answer to the amounts of shag and sculptured carpet to be produced. (5 marks)