Q A medical company manufactures three types of chemicals, chemical 1, chemical 2 and chemical 3. Chemical 1 requires 5 mg (miligrams) of raw material and 10 minutes of labor time for per unit production. Chemical 2 requires 6 mg of raw material and 12 minutes of labor time for per unit production. Unit chemical 3 requires 7 units of raw material and 13 minutes of labor time for per unit production. The company has 600 mg of raw material and 1200 minutes of labor time available. By selling a unit of each chemical, the company earns the profits of $5, $7 and $8 for chemical 1, chemical 2 and chemical 3, respectively. Besides, the demands for those chemicals are expected as 200 mg, 200 mg and 150 mg. The company has established the following goals, in order of their importance:
1) Achieve a minimum profit of $300.
2) The company wants to eliminate overutilization of raw material.
3) The company wants to avoid underutilization of labor time.
4) The company wants to limit the additional labor time with 80 minutes.
5) The company wants to minimize the unmet demand of chemical 1, chemical 2 and chemical 3. However, this goal should be weighted according to the profits of the chemicals.
Formulate a goal programming model to determine how many of each type of chemicals should be produced.