Question: Coffee Blending and Sales: 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: Argentine Abundo, Peruvian Colmado, Brazilian Maximo, and Chilean Saboro. The table below summarizes the very precise recipes for the final coffee blends, the cost and availability 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.
The processor's plant can handle no more than 100,000 pounds per week, and Hill-O-Beans would like to operate at capacity. There is no problem in selling the final blends, although the Marketing Department requires minimum production levels of 10,000, 25,000, and 30,000 pounds, respectively, for the hotel, restaurant, and market blends.
|
Component
|
Hotel
|
Restaurant
|
Market
|
Cost per pound
|
Pounds
available
|
|
Abundo
|
20%
|
35%
|
10%
|
$0.60
|
40,000
|
|
Colmado
|
40%
|
15%
|
35%
|
$0.80
|
25,000
|
|
Maximo
|
15%
|
20%
|
40%
|
$0.55
|
20,000
|
|
Saboro
|
25%
|
30%
|
15%
|
$0.70
|
45,000
|
|
Wholesale price
|
|
|
|
|
|
|
per pound
|
$1.25
|
$1.50
|
$1.40
|
|
|
(a) In order to maximize weekly profit, how many pounds of each component should be purchased?
(b) What is the shadow price (from the Sensitivity Report) on the availability of Maximo beans?
(c) How much (per pound) should Hill-O-Beans be willing to pay for additional pounds of Maximo beans in order to raise total profit?