A company builds sailboats and has a model that determines how many sailboats to build during each of the next four quarters to meet demand on time. The demand during each of the four quarters is as follows: 1st quarter is 160 sailboats, 2nd quarter is 240 sailboats, 3rd quarter is 300 sailboats and 4th quarter is 100 sailboats. At the beginning of the 1st quarter, the company has an inventory of 40 sailboats. The model assumes 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?