Q An electronics company manufactures two types of products: component 1 and component 2. Producing component 1, requires 1 unit of raw material 1, 3 units of raw material 2, and 2 hours of labor time. Producing a component 2. 2 units of raw material 1, 2 units of raw material 2, and 3 hours of labor time are required. Profits per product are $8 and $12 for component 1 and component 2, respectively. The company has available 40 units of raw material 1,50 units of raw material 2 and 70 hours of labor time. Besides, the company expects the demand for component 1 is 10 and the demand for component 2 to be 15. The company has established the following goals, in order of their importance
1) The company wants to avoid underutilization of labor hours.
2) The company wants to limit the additional labor hours to 10 hours.
3) The company sets a minimum amount of protit S500
4) The company does not want have too many units left on hand for raw material 1
5) The company wants to avoid overutilization of raw material 2.
6) The company wants to minimize the unmet demand of component 1 and component 2. However, this goal should be weighted according to the profits of the components. Formulate a goal programming model to determine how many of each type of component should be produced
