Question
4. Blending Coffee . The Great Canadian Coffee Company imports coffee beans and is attempting to create a coffee blend that will maximize profit and
4. Blending Coffee. The Great Canadian Coffee Company imports coffee beans and is attempting to create a coffee blend that will maximize profit and appeal to Canadian tastes. Two major characteristics of coffee are acidity and body. Consumer studies have indicated that Canadians prefer a coffee blend that is not overly acidic and that can be characterized as full- bodied. The company packages its coffee blends in 150 gram vacuum- sealed bags and sells 10 000 bags a day. Each bag produces $ 6.20 sales revenue. The four types of coffee beans that the company imports for blending have the following characteristics:
Coffee Type | Cost/kg | Acidity coefficient | Body coefficient | Availability(kg/day) |
Brazilian | 4.60 | 7 | 4 | 4000 |
Columbian | 4.40 | 2 | 6 | 5000 |
Jamaican | 3.80 | 6 | 3 | 3000 |
Hawaiian | 3.60 | 3 | 5 | 4000 |
The company has decided that a Canadian blend should have an average acidity coefficient that is no more than 5 and an average body coefficient that is at least 4. Also, each 150 gram bag should contain at most 30% Jamaican coffee and at least 20% Colombian coffee.
- Formulate the Great Canadian Coffee Companys blending problem as a linear program.
- BONUS. Solve the problem using Excel Solver and answer the following questions:
- How many grams of each type of coffee beans should be mixed in a 150 gram bag?
- What is the total daily profit?
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