6. On December 31, the ABC Company planned next year’s sales to be:

Currently, the firm has 12 employees, each producing up to 1,000 units per quarter and earning $2,000 per quarter. The firm estimates its inventory carrying cost to be $2 per unit of ending inventory per quarter and its hiring or layoff costs to be $1,600 per employee. The firm could increase production by working overtime, but overtime work is limited to 25 percent of the regular production rate (or 250 units per employee per quarter). Overtime work is paid at the rate of 1.5 times the regular pay rate. Unused regular time costs the firm $4.16 per hour. (Assume there are 60 eight-hour days per quarter.) The company currently has an inventory of 1,000 units and wishes to have an ending inventory of 1,000 units at the end of the year. The company does not plan to incur inventory shortages.

a. Develop the total cost equation for this problem.

b. Formulate this problem for solution, using LP.

c. What is the total cost of a production plan that assumes a constant production rate (include both regular and overtime production) and level workforce (assume 12 workers) each quarter?

d. Compare the cost of the production plan in c to one based on a production rate equal to sales in each quarter. Which has the lowest cost?

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Quarter 123+ Planned Sales 9,000 units 12,000 16,000 4 12,000 49,000