
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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![### Coffee Blending Problem
Deluxe coffee is to be mixed with regular coffee to make at least 48 pounds of a blended coffee. The mixture must contain at least 9 pounds of deluxe coffee. Deluxe coffee costs $5 per pound and regular coffee $4 per pound. How many pounds of each kind of coffee should be used to minimize costs?
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**Question:**
To attain the minimum cost, use [ ] pounds of deluxe coffee and [ ] pounds of regular coffee.
### Explanation
This problem involves finding the optimal blend of two types of coffee to minimize costs while satisfying specified constraints. In mathematical terms, it's an optimization problem with constraints.
1. **Constraints:**
- Total weight: at least 48 pounds
- Minimum deluxe coffee: at least 9 pounds
2. **Costs:**
- Deluxe coffee: $5 per pound
- Regular coffee: $4 per pound
### Solution Approach
To solve such a problem, we use linear programming techniques or a systematic approach to test possible combinations that satisfy the constraints.
1. Let the amount of deluxe coffee be \( D \) pounds.
2. Let the amount of regular coffee be \( R \) pounds.
**Constraints:**
- \( D + R \geq 48 \)
- \( D \geq 9 \)
**Objective:**
Minimize cost, \( C \):
\[ C = 5D + 4R \]
By substituting potential values and ensuring all conditions are met, we can find the values of \( D \) and \( R \) that result in the minimum cost. The solution should be presented by filling the blanks in the question:
**To attain the minimum cost, use [ ] pounds of deluxe coffee and [ ] pounds of regular coffee.**
This transcription and explanation would help students understand the problem, constraints, and the approach to solve the optimization problem.](https://content.bartleby.com/qna-images/question/132027c3-2ed1-42c8-912e-c4831680baff/8fbb7093-41f5-4fb8-9de1-befc95dbbb31/wsf9dii_thumbnail.png)
Transcribed Image Text:### Coffee Blending Problem
Deluxe coffee is to be mixed with regular coffee to make at least 48 pounds of a blended coffee. The mixture must contain at least 9 pounds of deluxe coffee. Deluxe coffee costs $5 per pound and regular coffee $4 per pound. How many pounds of each kind of coffee should be used to minimize costs?
---
**Question:**
To attain the minimum cost, use [ ] pounds of deluxe coffee and [ ] pounds of regular coffee.
### Explanation
This problem involves finding the optimal blend of two types of coffee to minimize costs while satisfying specified constraints. In mathematical terms, it's an optimization problem with constraints.
1. **Constraints:**
- Total weight: at least 48 pounds
- Minimum deluxe coffee: at least 9 pounds
2. **Costs:**
- Deluxe coffee: $5 per pound
- Regular coffee: $4 per pound
### Solution Approach
To solve such a problem, we use linear programming techniques or a systematic approach to test possible combinations that satisfy the constraints.
1. Let the amount of deluxe coffee be \( D \) pounds.
2. Let the amount of regular coffee be \( R \) pounds.
**Constraints:**
- \( D + R \geq 48 \)
- \( D \geq 9 \)
**Objective:**
Minimize cost, \( C \):
\[ C = 5D + 4R \]
By substituting potential values and ensuring all conditions are met, we can find the values of \( D \) and \( R \) that result in the minimum cost. The solution should be presented by filling the blanks in the question:
**To attain the minimum cost, use [ ] pounds of deluxe coffee and [ ] pounds of regular coffee.**
This transcription and explanation would help students understand the problem, constraints, and the approach to solve the optimization problem.
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