Q A textile company manufactures three types of clothes, shirts, jackets and skirts. A shirt production requires 10 units of cotton and 30 minutes of labor time. A jacket production requires 15 units of cotton and 50 minutes of labor time. A skirt production requires 18 units of cotton and 45 units of labor time. The company has 600 units of cotton and 2000 minutes of labor time available. By selling a shirt, a jacket, and a skirt, the company earns $20, $30, and $25 of profit, respectively. Besides, the demand for shirts, jackets, and skirts are expected as 5, 8 and 10, respectively. The company has established the following goals, in order of their importance:
1) The company wants to avoid the underutilization of cotton.
2) The company wants to achieve a profit of 550.
3) The company wants to minimize the unmet demand for shirts, jackets,s, and skirts. However, this goal should be weighted according to the profits of the clothes.
4) The company wants to avoid underutilization of labor time.
5) The company wants to limit the overtime labor time by 100 minutes. Formulate a goal programming model to determine how many of each type of clothes should be produced.
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