San Diego Boats (SDB) must determine how many sailboats should be produced during each of the next four quarters (one quarter = three months). The demand during each of the next four quarters is as follows: first quarter 40 sailboats, second quarter 60, third quarter 75 and fourth quarter 25 sailboats. SDB must meet the demands on time. At the beginning of the first quarter
SDB has an inventory of 10 sailboats. At the beginning of each quarter SDB must decide how many sailboats should be produced during the quarter. For simplicity we assume that sailboats manufactured during a quarter can be used to meet demand for that quarter. During each quarter SDB can produce up to 40 sailboats with regular labor at a total cost of $400 per boat and by having employees work overtime during a quarter SDB 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 carrying or holding cost of $20 per sailboat is incurred.
a. Use LP to formulate the problem of production scheduling that minimizes total cost.
b. Solve the problem in Excel Solver. Which constraint has the highest shadow price?
Explain what that means.