solution

Sailco must determine how many sailboats to produce during each of the next four quarters. At the beginning of the first quarter, Sailco has an inventory of 10 sailboats. Sailco must meet demand on time. The demand during each of the next four quarters is as follows:

1st Quarter	2nd Quarter	3rd Quarter	4th Quarter
40	60	75	75

During each quarter, Sailco can produce up to 50 sailboats with regular-time employees, at a labor cost of $400 per sailboat. By having employees work overtime during a quarter, Sailco can produce unlimited additional sailboats with overtime labor at a 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 for each boat in the inventory. To avoid stockout, Sailco wants to maintain an inventory of at least 5 boats at each quarter.

Let r_j = amount of sailboat produced during regular shift in quarter j, j = 1,2,3,4

o_j = amount of sailboat produced during overtime shift in quarter j

I_j = inventory at the end of quarter j

Correct formulation of the demand constraint for period 3 is:

		r4 + o4 + I4 – I3 = 75.
		r3 + o3 + I2 – I3 = 75.
		r4 + o4– I3 – I4 = 75.
		r3 + o3– I2 + I3 = 75.