The Oregon Atlantic Company produces two kinds of paper—newsprint and white wrapping paper (butcher paper). It requires 5 minutes to produce a yard of newsprint and 8 minutes to produce a yard of wrapping paper. The company has 4,800 minutes of normal production capacity available each week. The profit is $0.20 for a yard of newsprint and $0.25 for a yard of wrapping paper. The weekly demand is for 500 yards of newsprint and 400 yards of wrapping paper.
The company has established the following goals, in order of priority:
(1) Limit overtime to 480 minutes.
(2) Achieve a profit of $300 each week.
(3) Fulfill the demand for the products in order of magnitude of their profits.
(4) Avoid underutilization of production capacity.
a. Formulate a goal programming model to determine the number of yards of each type of paper to produce weekly to satisfy the various goals.
b. Solve the goal programming model by using the computer.