Sailco Corporation must determine how many sailboats to produce during each of the next 4 quarters.

The demand during each of the next four quarters is as follows: first quarter, 40 sailboats; second quarter, 60 sailboats; third quarter, 75 sailboats; fourth quarter, 25 sailboats. Sailco must meet demands on time. At the beginning of the first quarter, Sailco has an inventory of 10 sailboats. At the beginning of each quarter, Sailco must decide how many sailboats to produce during that quarter. For simplicity, assume that sailboats manufactured during a quarter can be used to meet demand for that quarter. During each quarter, Sailco can produce up to 40 sailboats with regulartime labor at a total cost of $400 per sailboat. By having employees work overtime during a quarter, Sailco can produce additional sailboats with overtime labor at a total cost of $450 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 $20 per sailboat is incurred.

a. Determine a production schedule to minimize the sum of production and inventory holding costs during the next 4 quarters.

b. Suppose Sailco wants to see whether any changes in the $20 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 4-month interval of systematic changes in the unit holding cost. (Assume that even though the unit holding cost changes, it is still constant over the 4-month interval.) Are there any (nonnegative)
unit holding costs that would induce Sailco to hold more inventory than it holds when the holding cost is $20? Are there any unit holding costs that would induce Sailco to hold less inventory than it holds when the holding cost is $20?