Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 28

In Problem:
a. If Starbright Coffee Shop could get 1 more pound of coffee, which one should it be What would be the effect on sales of getting 1 more pound of this coffee Would it benefit the shop to increase its brewing capacity from 30 gallons to 40 gallons
b. If the shop spent $20 per day on advertising that would increase the relative demand for Pomona to twice that of Coastal, should it be done
Problem
Starbright Coffee Shop at the Galleria Mall serves two coffee blends it brews on a daily basis, Pomona and Coastal. Each is a blend of three high-quality coffees from Colombia, Kenya, and Indonesia. The coffee shop has 6 pounds of each of these coffees available each day. Each pound of coffee will produce sixteen 16-ounce cups of coffee. The shop has enough brewing capacity to brew 30 gallons of these two coffee blends each day. Pomona is a blend of 20% Colombian, 35% Kenyan, and 45% Indonesian, while Coastal is a blend of 60% Colombian, 10% Kenyan, and 30% Indonesian. The shop sells 1.5 times more Pomona than Coastal each day. Pomona sells for $2.05 per cup, and Coastal sells for $1.85 per cup. The manager wants to know how many cups of each blend to sell each day in order to maximize sales.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.