Hill-O-Beans Coffee Company blends 4 component beans into 3 final blends of coffee: one is sold to luxury hotels, another to restaurants, and third to supermarkets for store label brands. Company has 4 reliable bean supplies: Robusta, Javan Arabica, Liberica, and Brazilian Arabica. Following table summarizes very precise recipes for final coffee blends, cost and availablilty information for four components, and wholesale price per pound of final blends. Percentages indicate fraction of each component to be used in every 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
Processor's plant can handle no more than 100,000 pounds per week, but there is virtually unlimited demand for final blends. Though, marketing department needs minimum production levels of 10,000, 25,000, and 30,000 pounds, respectively, for hotel, restaurant, and market blends.
a. To maiximize weekly profit, how many pounds of every component must be bought?
b. Find economic value of the additional pound's worth of plant capacity?
c. How much (per pound) must Hill-O-Beans be eager to pay for extra pounds of Liberica to raise total profit?
d. Create the graph to illustrate how optimal profit differs with minimum weekly production level of hotel blend.
e. Create the graph to illustrate how optimal profit differs with unit cost of Robusta beans.