Business Analytics 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, 1200 shirts and 1300 pairs of pants; month 2, 1700 shirts and 2000 pairs of pants. During each month the following resources are available: month 1, 6000 square yards of cloth; month 2, 9000 square yards of cloth. In addition, cloth that is available during month 1 and is not used can be used during month 2. The cost of cloth was $3 per square metre. During each month it costs $10 to produce an article of clothing with regular-time labor and $16 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 $5 per article of clothing is incurred.

Required:

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. Indicate the number of productions for shirts and pants in each month, number of ending inventory for each shirt and pants in each month and total costs.

b. There will be a shortage in the supplies of cloth during the month of October. Use a one-way SolverTable to investigate the effect of fabric shortage to the lowest of 3,000, then increase the number by 500 to 10,000 square metres. Explain the effect of cloth shortage to that company.

c. Use a two-way SolverTable to investigate the effect on total cost of two simultaneous changes. The first change is to increase overtime cost to $20 and reduce it to $10 in increments of $2. Secondly, change the production capacity (currently 2,500) from 1,500 to 5,000 in increment of 500. Explain the net effect on total cost because of changes in each individual variable. What changes would you recommend for production capacity?