3.Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are given in the following table:
Bean Cost/Pound Available Pounds
1 $0.50 500
2 $0.70 600
3 $0.45 400
Consumer tests with coffee products were used to provide quality ratings on a 0-to-100 scale, with higher ratings indicating higher quality. Product-quality stan¬dards for the blended coffee require a consumer rating for aroma to be at least 75 and a consumer rating for taste to be at least 80. The aroma and taste ratings for coffee made from 100 percent of each bean are given in the following table:
Bean Aroma Rating Taste Rating
1 75 86
2 85 88
3 60 75
It is assumed that the aroma and taste attributes of the coffee blend will be a weighted average of the attributes of the beans used in the blend.
a.What is the minimum-cost blend of the three beans that will meet the quality standards and provide 1,000 pounds of the blended coffee product?
b.What is the bean cost per pound of the coffee blend?
a. The minimum-cost blend of the three beans that will meet the quality standards and provide 1,000 pounds of the blended coffee product is: 500 pounds of Bean 1, 300 pounds of Bean 2, and 200 pounds of Bean 3.
You’re availability constraints are all met with a total of 1000 pounds with an aroma rating of 75 and a taste rating of 84.4
b. The bean cost per pound of the coffee blend is: $.55
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