The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs. Suppose that a manufacturer of widgets has fixed costs of $7000 per month and that the variable cost is $16 per widget (so it costs $16 to produce 1 widget). (a) Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. (Use N as the number of widgets produced in a month.) C= (b) Express using functional notation the total cost if there are 200 widgets produced in a month. C( Calculate the total cost if there are 200 widgets produced in a month. $
The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs. Suppose that a manufacturer of widgets has fixed costs of $7000 per month and that the variable cost is $16 per widget (so it costs $16 to produce 1 widget). (a) Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. (Use N as the number of widgets produced in a month.) C= (b) Express using functional notation the total cost if there are 200 widgets produced in a month. C( Calculate the total cost if there are 200 widgets produced in a month. $
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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![### Understanding Total Cost in Manufacturing
The **total cost** \( C \) for a manufacturer during a given time period is a function of the number \( N \) of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer’s *fixed costs* (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the *variable cost*.
To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs.
#### Example Problem
Suppose that a manufacturer of widgets has fixed costs of **$7000** per month and that the variable cost is **$16** per widget (so it costs **$16** to produce 1 widget).
1. **Formulating the Total Cost Function**
(a) Use a formula to express the total cost \( C \) of this manufacturer in a month as a function of the number of widgets produced in a month. (Use \( N \) as the number of widgets produced in a month.)
\[
C = \text{\$7000} + 16N
\]
2. **Calculating Specific Total Costs**
(b) Express using functional notation the total cost if there are **200** widgets produced in a month.
\[
C(200) = 7000 + 16 \cdot 200
\]
Calculate the total cost if there are **200** widgets produced in a month.
\[
C(200) = 7000 + 3200 = 10200
\]
Thus, the total cost if there are 200 widgets produced in a month is **$10,200**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d91cf51-36b6-472d-8082-aa48d6da434d%2F58a84a2e-e5ae-4a9a-a1cc-1295f2523855%2Fu5ylyin_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Total Cost in Manufacturing
The **total cost** \( C \) for a manufacturer during a given time period is a function of the number \( N \) of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer’s *fixed costs* (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the *variable cost*.
To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs.
#### Example Problem
Suppose that a manufacturer of widgets has fixed costs of **$7000** per month and that the variable cost is **$16** per widget (so it costs **$16** to produce 1 widget).
1. **Formulating the Total Cost Function**
(a) Use a formula to express the total cost \( C \) of this manufacturer in a month as a function of the number of widgets produced in a month. (Use \( N \) as the number of widgets produced in a month.)
\[
C = \text{\$7000} + 16N
\]
2. **Calculating Specific Total Costs**
(b) Express using functional notation the total cost if there are **200** widgets produced in a month.
\[
C(200) = 7000 + 16 \cdot 200
\]
Calculate the total cost if there are **200** widgets produced in a month.
\[
C(200) = 7000 + 3200 = 10200
\]
Thus, the total cost if there are 200 widgets produced in a month is **$10,200**.
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