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 recipes for the final coffee blends are summarized in the table below, along with the price and availability of each raw material. The percentages indicate the fraction of each component used in each blend.

The wholesale price of each product is $1.25/lb for hotel blend, $1.50/lb for restaurants, and $1.40/lb for supermarkets. The processing plant has a maximum capacity of 25,000 lb/week. There is no shortage of demand for any of the blends, although the marketing department requires minimum production levels of 5,000, 6,250, and 10,000 lbs/week, respectively, for the hotel, restaurant, and supermarket blends.
Formulate as a linear program to determine the mixture that maximizes Hill-O-Beans profit. How many pounds of each component should be purchased and what is the maximum weekly profit?

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Max Wkly Avail (Ibs) Robusta Javan Arabica 40% Liberica Brazilian Arabica 25% 1000 $0.60 5,000 35% S0.80 7,500 4000 $0.55 5,000 1590 $0.70 5,000 20% 35% 15% 20% 30% 15%