# Question

A textile company produces shirts and pants. Each shirt requires two square yards of cloth, and each pair of pants requires three square yards of cloth. During the next two months the following demands for shirts and pants must be met (on time): month 1, 1000 shirts and 1500 pairs of pants; month 2, 1200 shirts and 1400 pairs of pants. During each month the following resources are available: month 1, 9000 square yards of cloth; month 2, 6000 square yards of cloth. In addition, cloth that is available during month 1 and is not used can be used during month 2. During each month it costs $8 to produce an article of clothing with regular-time labor and $12 with overtime labor.

During each month a total of at most 2500 articles of clothing can be produced with regular-time labor, and an unlimited number of articles of clothing can be produced with overtime labor. At the end of each month, a holding cost of $3 per article of clothing is incurred.

a. Determine how to meet demands for the next two months (on time) at minimum cost. Assume that 100 shirts and 200 pairs of pants are already in inventory at the beginning of month 1.

b. Use a two-way SolverTable to investigate the effect on total cost of two simultaneous changes. The first change is to allow the ratio of overtime to regular time production cost (currently $16/$8 = 2) to decrease from 20% to 80% in increments of 20%, while keeping the regular time cost at $8. The second change is to allow the production capacity each month (currently 2500) to decrease by 10% to 50% in increments of 10%. The idea here is that less regular-time capacity is available, but overtime becomes relatively cheaper. Is the net effect on total cost positive or negative?

During each month a total of at most 2500 articles of clothing can be produced with regular-time labor, and an unlimited number of articles of clothing can be produced with overtime labor. At the end of each month, a holding cost of $3 per article of clothing is incurred.

a. Determine how to meet demands for the next two months (on time) at minimum cost. Assume that 100 shirts and 200 pairs of pants are already in inventory at the beginning of month 1.

b. Use a two-way SolverTable to investigate the effect on total cost of two simultaneous changes. The first change is to allow the ratio of overtime to regular time production cost (currently $16/$8 = 2) to decrease from 20% to 80% in increments of 20%, while keeping the regular time cost at $8. The second change is to allow the production capacity each month (currently 2500) to decrease by 10% to 50% in increments of 10%. The idea here is that less regular-time capacity is available, but overtime becomes relatively cheaper. Is the net effect on total cost positive or negative?

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