# Question

A company that builds sailboats wants to determine how many sailboats to build during each of the next four quarters. The demand during each of the next four quarters is as follows: first quarter, 160 sailboats; second quarter, 240 sailboats; third quarter, 300 sailboats; fourth quarter, 100 sailboats. The company must meet demands on time. At the beginning of the first quarter, the company has an inventory of 40 sailboats.

At the beginning of each quarter, the company must decide how many sailboats to build during that quarter. For simplicity, assume that sailboats built during a quarter can be used to meet demand for that quarter. During each quarter, the company can build up to 160 sailboats with regular time labor at a total cost of $1600 per sailboat. By having employees work overtime during a quarter, the company can build additional sailboats with overtime labor at a total cost of $1800 per sailboat. At the end of each quarter (after production has occurred and the current quarter’s demand has been satisfied), a holding cost of $80 per sailboat is incurred.

a. Determine a production schedule to minimize the sum of production and inventory holding costs during the next four quarters.

b. Use SolverTable to see whether any changes in the $80 holding cost per sailboat could induce the company to carry more or less inventory. Revise your model so that SolverTable can be used to investigate the effects on ending inventory during the four-quarter period of systematic changes in the unit holding cost. Are there any (nonnegative) unit holding costs that would induce the company to hold more inventory than it holds when the holding cost is $80? Are there any unit holding costs that would induce the company to hold less inventory than it holds when the holding cost is $80?

At the beginning of each quarter, the company must decide how many sailboats to build during that quarter. For simplicity, assume that sailboats built during a quarter can be used to meet demand for that quarter. During each quarter, the company can build up to 160 sailboats with regular time labor at a total cost of $1600 per sailboat. By having employees work overtime during a quarter, the company can build additional sailboats with overtime labor at a total cost of $1800 per sailboat. At the end of each quarter (after production has occurred and the current quarter’s demand has been satisfied), a holding cost of $80 per sailboat is incurred.

a. Determine a production schedule to minimize the sum of production and inventory holding costs during the next four quarters.

b. Use SolverTable to see whether any changes in the $80 holding cost per sailboat could induce the company to carry more or less inventory. Revise your model so that SolverTable can be used to investigate the effects on ending inventory during the four-quarter period of systematic changes in the unit holding cost. Are there any (nonnegative) unit holding costs that would induce the company to hold more inventory than it holds when the holding cost is $80? Are there any unit holding costs that would induce the company to hold less inventory than it holds when the holding cost is $80?

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