Determine minimum-cost blend of three beans

Question

Hilltop Coffee produces the coffee product by blending 3 kinds of coffee beans. Cost per pound and available pounds of every bean are given in table:

Bean Cost/Pound     Available Pounds

1          $0.50          500

2          $0.70          600

3          $0.45          400

Consumer tests with coffee products were utilized to give quality ratings on 0-to-100 scale, with higher ratings pointing higher quality. Product-quality stan­dards for blended coffee need the consumer rating for aroma to be at least 75 and consumer rating for taste to be at least 80. Aroma and taste ratings for coffee made from 100% of every bean are provided in given table:

Bean    Aroma Rating   Taste Rating

1            75                  86

2            85                  88

3            60                  75

It is supposed that aroma and taste attributes of coffee blend will be the weighted average of attributes of beans used in blend.

i) Determine minimum-cost blend of three beans which will meet quality standards and give 1,000 pounds of blended coffee product?

ii) Determine bean cost per pound of coffee blend?