Problem #2

Shoeco must meet (on time) the following demands for pairs of shoes: month 1 300; month 2 500; month 3 100; and month 4 100. At the beginning of month 1, 50 pairs of shoes are on hand, and Shoeco has three workers. A worker is paid $1500 per month. Each worker can work up to 160 hours per month before he receives overtime. During any month, each worker may be required to work up to 20 hours of overtime; workers are paid $25 per hour for overtime labor. It takes 4 hours of labor and $5 of raw material to produce each pair of shoes. At the beginning of each month, workers can be hired or fired. Each hired worker costs $1600 (this cost is in addition to workers salaries), and each fired worker costs $2000 . At the end of each month, a holding cost of $30 per pair of shoes is assessed. Formulate an LP that can be used to minimize the total cost of meeting the next four months demands. Solve the LP using GAMS (submit your GAMS file, and provide details of the optimal solution). Use the GAMS output to answer the following questions without rerunning GAMS.

A. If overtime labor during month 1 costs $16 per hour, should any overtime labor be used?

B. If the cost of firing workers during month 3 were $1800, what would be the new optimal solution?

C. By how much would total costs be reduced if demand in month 1 were 100 pairs of shoes?

D. What would be the total cost if the company had 5 workers at the beginning of month 1 (before month 1s hiring or firing takes place)?