**31. Modeling in manufacturing.**A manufacturer of golf clubs finds that the fixed costs are $5780 per week and the cost of producing each set of clubs is $73.00. Each set of clubs can be sold for $243.00. a. Write the revenue function. b. Write the cost function. c. Write the profit function. d. Find the break-even point.**Explanation:**1. **Revenue Function**: The revenue function $R(x)$ can be formulated based on the selling price per set of clubs. If each set is sold for $243.00 and if $x$ represents the number of sets sold, the revenue function is: \[ R(x) = 243x \]2. **Cost Function**: The cost function $C(x)$ is based on the fixed costs and the variable costs per set of clubs. With fixed costs of $5780 per week and a production cost of $73.00 per set, the cost function is: \[ C(x) = 5780 + 73x \]3. **Profit Function**: The profit function $P(x)$ is found by subtracting the total cost from the total revenue. Using the revenue function $R(x)$ and the cost function $C(x)$, the profit function is: \[ P(x) = R(x) - C(x) = 243x - (5780 + 73x) \] Simplifying, we get: \[ P(x) = 243x - 5780 - 73x = 170x - 5780 \]4. **Break-even Point**: To find the break-even point, we need to determine the value of $x$ when the revenue equals the cost. This occurs when $R(x) = C(x)$: \[ 243x = 5780 + 73x \] Solving for $x$: \[ 243x - 73x = 5780 \] \[ 170x = 5780 \] \[ x = \frac{5780}{170} \approx 34 \] Therefore, the break-even point is when approximately 34 sets of clubs are produced

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that the fixed costs are $5780 per week and the cost of producing each set of clubs is $73.00. Each set of clubs can be sold for $243.00. a. Write the revenue function. b. Write the cost function. c. Write the profit function. d. Find the break-even point.

that the fixed costs are $5780 per week and the cost of producing each set of clubs is $73.00. Each set of clubs can be sold for $243.00. a. Write the revenue function. b. Write the cost function. c. Write the profit function. d. Find the break-even point.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

**31. Modeling in manufacturing.**

A manufacturer of golf clubs finds that the fixed costs are $5780 per week and the cost of producing each set of clubs is $73.00. Each set of clubs can be sold for $243.00.

a. Write the revenue function.
b. Write the cost function.
c. Write the profit function.
d. Find the break-even point.

**Explanation:**

1. **Revenue Function**: The revenue function $R(x)$ can be formulated based on the selling price per set of clubs. If each set is sold for $243.00 and if $x$ represents the number of sets sold, the revenue function is:
\[
R(x) = 243x
\]

2. **Cost Function**: The cost function $C(x)$ is based on the fixed costs and the variable costs per set of clubs. With fixed costs of $5780 per week and a production cost of $73.00 per set, the cost function is:
\[
C(x) = 5780 + 73x
\]

3. **Profit Function**: The profit function $P(x)$ is found by subtracting the total cost from the total revenue. Using the revenue function $R(x)$ and the cost function $C(x)$, the profit function is:
\[
P(x) = R(x) - C(x) = 243x - (5780 + 73x)
\]
Simplifying, we get:
\[
P(x) = 243x - 5780 - 73x = 170x - 5780
\]

4. **Break-even Point**: To find the break-even point, we need to determine the value of $x$ when the revenue equals the cost. This occurs when $R(x) = C(x)$:
\[
243x = 5780 + 73x
\]
Solving for $x$:
\[
243x - 73x = 5780
\]
\[
170x = 5780
\]
\[
x = \frac{5780}{170} \approx 34
\]
Therefore, the break-even point is when approximately 34 sets of clubs are produced

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