A coffee manufacturer is interested in blending five types of coffee beans into a fine blend of 120,000 pounds of coffee. The five component beans cost $2, $3, $4, $2 and $2 per pound respectively. The budget for purchasing the five components is $300,000. In blending the coffee, three restrictions have been stated: (1) the combination of 1 and 2 should constitute exactly half of the final blend; (2) components 1 and 5 together should constitute exactly 25 percent of the final blend; and (3) the amount of component 4 used in the blend should be exactly three times the amount used of component 3. (a) Formulate the system of equations which states all the requirements in this blending problem. (b) How many pounds of each component should be used in the final blend?
A coffee manufacturer is interested in blending five types of coffee beans into a fine blend of 120,000 pounds of coffee. The five component beans cost $2, $3, $4, $2 and $2 per pound respectively. The budget for purchasing the five components is $300,000. In blending the coffee, three restrictions have been stated: (1) the combination of 1 and 2 should constitute exactly half of the final blend; (2) components 1 and 5 together should constitute exactly 25 percent of the final blend; and (3) the amount of component 4 used in the blend should be exactly three times the amount used of component 3. (a) Formulate the system of equations which states all the requirements in this blending problem. (b) How many pounds of each component should be used in the final blend?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 26EQ
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A coffee manufacturer is interested in blending five types of coffee beans into a fine blend of 120,000 pounds of coffee. The five component beans cost $2, $3, $4, $2 and $2 per pound respectively. The budget for purchasing the five components is $300,000. In blending the coffee, three restrictions have been stated: (1) the combination of 1 and 2 should constitute exactly half of the final blend; (2) components 1 and 5 together should constitute exactly 25 percent of the final blend; and (3) the amount of component 4 used in the blend should be exactly three times the amount used of component 3. (a) Formulate the system of equations which states all the requirements in this blending problem. (b) How many pounds of each component should be used in the final blend?
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