The East Midvale Textile Company produces denim and brushed-cotton cloth. The average production rate for both types of cloth is 1,000 yards per hour, and the normal weekly production capacity (running two shifts) is 80 hours. The marketing department estimates that the maximum weekly demand is for 60,000 yards of denim and 35,000 yards of brushed cotton. The profit is $3.00 per yard for denim and $2.00 per yard for brushed cotton. The company has established the following four goals, listed in order of importance:
(1) Eliminate underutilization of production capacity to maintain stable employment levels.
(2) Limit overtime to 10 hours.
(3) Meet demand for denim and brushed cotton weighted according to profit for each.
(4) Minimize overtime as much as possible.
a. Formulate a goal programming model to determine the number of yards (in 1,000-yard pots) to produce to satisfy the goals.
b. Solve this model by using the computer.