Problem: Hilltop Coffee manufactures a coffee product through blending three types of coffee beans. The cost per pound and accessible pounds are as follows: Bean 1: .50/pound 500 lbs accessible Bean 2: .70/pound 600 available lbs. Bean 3: .45/pound and 400 pounds accessible. Consumer tests with coffee products were used to offer quality ratings on a 0 to 100 scale, with higher ratings indicating higher quality. Product-quality standards for the blended coffee need a consumer rating for taste to be at least 75 and a consumer rating to be at least 80. The aroma and taste ratings for coffee made from 100% of each bean are given in the subsequent:
Bean 1: Aroma rating: 75 Taste rating: 86
Bean 2: Aroma rating: 85 Taste rating: 88
Bean 3: Aroma rating 60 Taste rating: 75
It is supposed that the aroma and taste attributes of coffee blend will be a weighted average of the attributes of the beans employed in the blend.
a. What is the minimum cost blend of the three beans that will meet the quality standards and provide 1000 pounds of the blended coffee product?
b. What is the bean per pound of the coffee blend?
c. Find out the aroma and taste ratings for the coffee blend.
d. If additional coffee were to be produced, what would be the expected cost per pound?