(b) How will an increase of $1 in the hourly labor rate affect the total cost? The total cost will increase by $14.5 x.
(b) How will an increase of $1 in the hourly labor rate affect the total cost? The total cost will increase by $14.5 x.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need help on part B.
![### Production Cost Analysis
The total cost of producing one unit of a product is given by the following function:
\[ C(x, y) = 80 + 0.3x^2 + 50y - xy \, \text{dollars} \]
where \( x \) is the hourly labor rate and \( y \) is the cost per pound of raw materials. The current hourly rate is \( \$27 \), and the raw materials cost \( \$2 \) per pound.
#### (a) Effect of a $1 Increase per Pound for Raw Materials:
**Question: How will an increase of $1 per pound for the raw materials affect the total cost?**
- **Answer:** The total cost will **increase** by **$23**. ✔️
#### (b) Effect of a $1 Increase in the Hourly Labor Rate:
**Question: How will an increase of $1 in the hourly labor rate affect the total cost?**
- **Answer:** The total cost will **increase** by **$14.5**. ❌
This analysis helps in understanding how changes in labor and material costs impact the overall production expenses.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8747d92-b055-4562-9504-cd72cffb1b1f%2F2d7ab9dc-08bf-4fb6-96c1-632e85697168%2F9uy0tlu_processed.png&w=3840&q=75)
Transcribed Image Text:### Production Cost Analysis
The total cost of producing one unit of a product is given by the following function:
\[ C(x, y) = 80 + 0.3x^2 + 50y - xy \, \text{dollars} \]
where \( x \) is the hourly labor rate and \( y \) is the cost per pound of raw materials. The current hourly rate is \( \$27 \), and the raw materials cost \( \$2 \) per pound.
#### (a) Effect of a $1 Increase per Pound for Raw Materials:
**Question: How will an increase of $1 per pound for the raw materials affect the total cost?**
- **Answer:** The total cost will **increase** by **$23**. ✔️
#### (b) Effect of a $1 Increase in the Hourly Labor Rate:
**Question: How will an increase of $1 in the hourly labor rate affect the total cost?**
- **Answer:** The total cost will **increase** by **$14.5**. ❌
This analysis helps in understanding how changes in labor and material costs impact the overall production expenses.
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