Last Cup Coffee Company (LCCC) is trying to determine the optimal way to produce its signature line of blended coffees, Prestige Light (PL), Prestige Medium (PM), Prestige Dark (PD) and Prestige Decaffeinated (DC). The coffees in the Prestige Line are blended from Indonesian (I), Colombian (C) and other (O) coffees. All these coffees contain a minimum of 50% Indonesian coffees and a maximum of 25% Colombian coffees. Coffee is roasted in 100-pound batches and it takes 1 hour to roast the Light, 1¼ hours for the Medium and 1½ hours for both the Dark and Decaffeinated coffees. Decaffeination adds $0.50 to the cost of making a pound the coffee. For the coming week, the firm has 3,000 pounds of Indonesian coffees and 2,000 pounds of Colombian coffees available in inventory, with no additional shipments expected this week. (Since these have already been purchased, we shall ignore their cost and treat them as sunk costs.) There is no limit on the availability of other coffee. The coffees are sold to the retail stores for $4.00 per pound for the Prestige light and Prestige Medium coffees, $4.50 for the Prestige Dark and $5.00 for the Prestige Decaffeinated. The cost of operating the roasting ovens is $120/hour and there are 40 hours of roasting time available. No more than 25% of the coffee will be Decaffeinated, and the Medium coffee must be at least 40% of the total production.
(a) Formulate this as a linear programming problem and solve it with a detailed description of your output. Please include all output information.
(b) How would your solution change if the roasting capacity could be doubled by adding a second shift? Please show model and changed results.
(c) Suppose that LCCC could sell unused Indonesian Coffee for $1.20 per pound and unused Colombian Coffee for $1.00 per pound. In addition, roasting oven time could be sold for $1.50. How would this change your formulation and solution to part (a)?