Hill-O-Beans Coffee Company blends four component beans into three final blends of coffee: one is sold to luxury hotels, another to restaurants, and the third to supermarkets for store label brands. The company has four reliable bean supplies: Robusta, Javan Arabica, Liberica, and Brazilian Arabica. The folowing tablesummarizes the very precise recipes for the final coffee blends, the cost and availablilty information for the four components, and the wholesale price per pound of the final blends. The percentages indicate the fraction of each component to be used in each blend.
Component Hotel Restaurant Market Cost/Pound Max Weekly Available (lbs)
Robusta 20% 35% 10% $0.60 40,000
Javan Arabica 40% 15% 35% $0.80 25,000
Liberica 15% 20% 40% $0.55 20,000
Brazilian Arabica 25% 30% 15% $0.70 45,000
Wholesale Price
Per Pound $1.25 $1.50 $1.40
The processor's plant can handle no more than 100,000 pounds per week, but there is virtually unlimited demand for the final blends. However, the marketing department requires minimum production levels of 10,000, 25,000, and 30,000 pounds, respectively, for the hotel, restaurant, and market blends.
a. In order to maiximize weekly profit, how many pounds of each component should be purchased?
b. What is the economic value os an additional pound's worth of plant capacity?
c. How much (per pound) should Hill-O-Beans be willing to pay for additional pounds of Liberica in order to raise total profit?
d. Construct a graph to show how optimal profit varies with the minimum weekly production level of the hotel blend.
e. Construct a graph to show how the optimal profit varies with the unit cost of Robusta beans.