The weekly cost C of producing x units in a manufacturing process is given by C(x) = 50x + 750. The number of units x produced in t hours is given by x(t) = 60t. (a) Find and interpret (C o x)(t). (Cox)(t) = O (Cox) (t) represents the production as a function of cost. O (Cox) (t) represents the cost of production as a function of time. (b) Find the cost of the units produced in 4 hours. $ (c) Find the time that must elapse in order for the cost to increase to $15,000. hr
The weekly cost C of producing x units in a manufacturing process is given by C(x) = 50x + 750. The number of units x produced in t hours is given by x(t) = 60t. (a) Find and interpret (C o x)(t). (Cox)(t) = O (Cox) (t) represents the production as a function of cost. O (Cox) (t) represents the cost of production as a function of time. (b) Find the cost of the units produced in 4 hours. $ (c) Find the time that must elapse in order for the cost to increase to $15,000. hr
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Title: Understanding Cost as a Function of Time in Manufacturing**
The weekly cost \( C \) of producing \( x \) units in a manufacturing process is given by \( C(x) = 50x + 750 \). The number of units \( x \) produced in \( t \) hours is given by \( x(t) = 60t \).
---
### (a) Find and Interpret \( (C \circ x)(t) \)
\[ (C \circ x)(t) = \]
\[ \boxed{50(60t) + 750} \]
\( \bigcirc \) \( (C \circ x)(t) \) represents the production as a function of cost.
\( \bigcirc \checked \) \( (C \circ x)(t) \) represents the cost of production as a function of time.
### (b) Find the Cost of the Units Produced in 4 Hours
\[ \$
\boxed{1230}
\]
### (c) Find the Time That Must Elapse in Order for the Cost to Increase to $15,000
\[ \boxed{4.85} \text{ hr} \]
---
Explanation:
**Equation Derivation:**
- Starting with the given:
\[ C(x) = 50x + 750 \]
\[ x(t) = 60t \]
- To find \((C \circ x)(t)\), we substitute \(x(t)\) into \(C(x)\):
\[
C(x(t)) = 50(60t) + 750 = 3000t + 750
\]
**Interpretation:**
- \( (C \circ x)(t) \) simplifies to the equation \(3000t + 750\), representing the cost of production as a function of time \( t \).
**Cost Calculation (Part b):**
- For \( t = 4 \) hours:
\[
C(x(4)) = 3000(4) + 750 = 12000 + 750 = 12750 \text{ dollars}
\]
**Time Calculation for $15,000 Cost (Part c):**
- Setting the cost equation to $15,000:
\[
3000t + 750 = 15000
\]
Solving for \( t \):
\[](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86020f22-4efe-437b-8b05-308770976ff7%2Fdfb3582d-d885-47b6-a5d7-7ddbebfccbeb%2Fuam9yvj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Cost as a Function of Time in Manufacturing**
The weekly cost \( C \) of producing \( x \) units in a manufacturing process is given by \( C(x) = 50x + 750 \). The number of units \( x \) produced in \( t \) hours is given by \( x(t) = 60t \).
---
### (a) Find and Interpret \( (C \circ x)(t) \)
\[ (C \circ x)(t) = \]
\[ \boxed{50(60t) + 750} \]
\( \bigcirc \) \( (C \circ x)(t) \) represents the production as a function of cost.
\( \bigcirc \checked \) \( (C \circ x)(t) \) represents the cost of production as a function of time.
### (b) Find the Cost of the Units Produced in 4 Hours
\[ \$
\boxed{1230}
\]
### (c) Find the Time That Must Elapse in Order for the Cost to Increase to $15,000
\[ \boxed{4.85} \text{ hr} \]
---
Explanation:
**Equation Derivation:**
- Starting with the given:
\[ C(x) = 50x + 750 \]
\[ x(t) = 60t \]
- To find \((C \circ x)(t)\), we substitute \(x(t)\) into \(C(x)\):
\[
C(x(t)) = 50(60t) + 750 = 3000t + 750
\]
**Interpretation:**
- \( (C \circ x)(t) \) simplifies to the equation \(3000t + 750\), representing the cost of production as a function of time \( t \).
**Cost Calculation (Part b):**
- For \( t = 4 \) hours:
\[
C(x(4)) = 3000(4) + 750 = 12000 + 750 = 12750 \text{ dollars}
\]
**Time Calculation for $15,000 Cost (Part c):**
- Setting the cost equation to $15,000:
\[
3000t + 750 = 15000
\]
Solving for \( t \):
\[
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