Formulate and solve the Sailco problem using IBM ILOG CPLEX Optimization Studio.

| (Winston 3.10, p. 99) Sailco must determine how many sailboats to produce in the next 4 quarters. The demand is known to be 40, 60, 75, and 25 boats. Sailco must meet its demands. At the beginning of the 1st quarter Sailco starts with 10 boats in inventory. Sailco can produce up to 40 boats with regular time labor at $400 per boat, or additional boats at $450 with overtime labor. Boats made in a quarter can be used to meet that quarter's demand or held in inventory for the next quarter at an extra cost of $20.00 per boat. Answer The decision variables are for t = 1,2,3,4 xt = # of boats in quarter t built in regular time yt = # of boats in quarter t built in overtime For convenience, introduce variables: it = # of boats in inventory at the end quarter t dt = demand in quarter t We are given that d1 = 40, d2 = 60, d3 = 75, d4 = 25, 10 = 10 Xt s 40, vt By logic i = 11-1+ X+ + yt-dt, Vt. Demand is met iff It 20, Vt (Sign restrictions Xt, yt 20, Vt) We need to minimize total cost z subject to these three sets of conditions where z = 400 (x1 + x2 + x3 + x4) + 450 (y1 + y2 + y2 + y4) + 20 (11 + 12 + 13 + 14)