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 lb per week, and Hill-O-Beans would like to operate at capacity, if possible. Selling the final blends is not a problem, although the Marketing Department requires minimum production levels of 10,000, 25,000, and 30,000 lb, respectively, for the hotel, restaurant and market blends.

a. To maximize weekly profit, how many pounds of each component should be purchased?

b. How would the optimal profit change if there were a 1000-lb increase in the availability of Abundo beans? Colmado? Maximo? Saboro?

Component (pounds) Abandon Commando Maxim Saber Wholesale price per pound Hotel 20% 40% 15% 25% $1.25 Rest 35% 15% 20% 30% $1.50 Market 10% 35% 40% 15% $1.40 Cost per pound $0.60 $0.80 $0.55 $0.70 Max. weekly availability 40,000 25,000 20,000 45,000