During the next four months, the SureStep Company must meet the following demands (with no backorders allowed) for pairs of shoes: 3000 in month 1, 5000 in month 2, 2000 in month 3, and 1000 in month 4. At the beginning of the first month, 500 pairs of shoes are on hand, and
SureStep has 100 workers. A worker is paid $1500 per month. Each worker can work up to 160 hours a month before he or she receives overtime. A worker can work up to 20 hours of overtime per month and is paid $13 per hour for overtime labor. It takes 4 hours of labor and $15 of raw materials to produce a pair of shoes. At the beginning of each month, workers can be hired or fired. Each hired worker costs $1600, and each fired worker costs $2000. At the end of each month, a holding cost of $3 per pair of shoes left in inventory is incurred. Develop and solve linear program to determine the optimal production plan for SureStep.