Sailco must meet demands on time. At the beginning for the first quarter, Sailco has an inventory of 10 sailboats. At the beginning of each quarter, Sailco decides how many sailboats to manufacture in that quarter, and we assume that sailboats manufactured in a quarter can be used to meet demand in that quarter. During each quarter Sailco can produced up to 40 sailboats with regular-time 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, a carrying or holding cost of $20 per sailboat is incurred. Use LP to determine a production schedule to minimize the sum of production and inventory costs during the next four quarters.