A firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost (in dollars) of manufacturing depends on the quantities, and y, produced at each factory, respectively, and is expressed by the joint cost function: C(x, y) = 6x² + 9xy + 8y² + 7800 A) If the company manufactures 150 units at Factory X and 160 units at Factory Y, what are the total Costs of production? Total Costs = $ BY Find an expression for the rate of change of costs with respect to units produced at Factory X. Write your answer as an expression, not an equation (i.e. do not use an = sign). Your expression = C) Find an expression for the rate of change of costs with respect to units produced at Factory Y. Write your answer as an expression, not an equation (i.e. do not use an = sign).
A firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost (in dollars) of manufacturing depends on the quantities, and y, produced at each factory, respectively, and is expressed by the joint cost function: C(x, y) = 6x² + 9xy + 8y² + 7800 A) If the company manufactures 150 units at Factory X and 160 units at Factory Y, what are the total Costs of production? Total Costs = $ BY Find an expression for the rate of change of costs with respect to units produced at Factory X. Write your answer as an expression, not an equation (i.e. do not use an = sign). Your expression = C) Find an expression for the rate of change of costs with respect to units produced at Factory Y. Write your answer as an expression, not an equation (i.e. do not use an = sign).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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![# Manufacturing Cost Analysis: Factory X and Factory Y
A firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost (in dollars) of manufacturing depends on the quantities, \( x \) and \( y \), produced at each factory, respectively, and is expressed by the joint cost function:
\[ C(x, y) = 6x^2 + 9xy + 8y^2 + 7800 \]
### Questions and Tasks
**A. Calculating Total Costs**
If the company manufactures 150 units at Factory X and 160 units at Factory Y, what are the total costs of production?
\[ \text{Total Costs} = \$ \]
**B. Rate of Change of Costs with Respect to Units Produced at Factory X**
Find an expression for the rate of change of costs with respect to units produced at Factory X. Write your answer as an expression, not an equation (i.e. do not use an = sign).
\[ \text{Your expression} = \]
**C. Rate of Change of Costs with Respect to Units Produced at Factory Y**
Find an expression for the rate of change of costs with respect to units produced at Factory Y. Write your answer as an expression, not an equation (i.e. do not use an = sign).
\[ \text{Your expression} = \]
**D. Rate of Change of Costs with Respect to Units Produced at Factory X (Given Production Levels)**
Find the rate of change of costs with respect to units produced at Factory X when 150 units have been produced at Factory X and 160 units have been produced at Factory Y.
\[ \text{Rate of change} = \quad \text{dollars per unit produced at } X. \]
**E. Rate of Change of Costs with Respect to Units Produced at Factory Y (Given Production Levels)**
Find the rate of change of costs with respect to units produced at Factory Y when 150 units have been produced at Factory X and 160 units have been produced at Factory Y.
\[ \text{Rate of change} = \quad \text{dollars per unit produced at } Y. \]
### Diagrams and Graphs Explanation
This exercise does not contain any graphs or diagrams to explain. It primarily focuses on mathematical expressions and rate of change calculations associated with production costs.
---
These calculations will aid the analysis of cost efficiency and assist managerial decisions regarding the distribution of production between](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F622a1a9e-da70-4332-96fa-d56b5a5adde8%2F8cd99d2f-abc9-44e0-8c58-dea15255ad9f%2Faglt29u_processed.png&w=3840&q=75)
Transcribed Image Text:# Manufacturing Cost Analysis: Factory X and Factory Y
A firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost (in dollars) of manufacturing depends on the quantities, \( x \) and \( y \), produced at each factory, respectively, and is expressed by the joint cost function:
\[ C(x, y) = 6x^2 + 9xy + 8y^2 + 7800 \]
### Questions and Tasks
**A. Calculating Total Costs**
If the company manufactures 150 units at Factory X and 160 units at Factory Y, what are the total costs of production?
\[ \text{Total Costs} = \$ \]
**B. Rate of Change of Costs with Respect to Units Produced at Factory X**
Find an expression for the rate of change of costs with respect to units produced at Factory X. Write your answer as an expression, not an equation (i.e. do not use an = sign).
\[ \text{Your expression} = \]
**C. Rate of Change of Costs with Respect to Units Produced at Factory Y**
Find an expression for the rate of change of costs with respect to units produced at Factory Y. Write your answer as an expression, not an equation (i.e. do not use an = sign).
\[ \text{Your expression} = \]
**D. Rate of Change of Costs with Respect to Units Produced at Factory X (Given Production Levels)**
Find the rate of change of costs with respect to units produced at Factory X when 150 units have been produced at Factory X and 160 units have been produced at Factory Y.
\[ \text{Rate of change} = \quad \text{dollars per unit produced at } X. \]
**E. Rate of Change of Costs with Respect to Units Produced at Factory Y (Given Production Levels)**
Find the rate of change of costs with respect to units produced at Factory Y when 150 units have been produced at Factory X and 160 units have been produced at Factory Y.
\[ \text{Rate of change} = \quad \text{dollars per unit produced at } Y. \]
### Diagrams and Graphs Explanation
This exercise does not contain any graphs or diagrams to explain. It primarily focuses on mathematical expressions and rate of change calculations associated with production costs.
---
These calculations will aid the analysis of cost efficiency and assist managerial decisions regarding the distribution of production between
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