Problems:
Statistical Analysis: Linear Optimization
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 Available Pounds
1 0.5 500
2 0.7 600
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 standards 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 Taste
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?