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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![**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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9e33d54-6f37-42c0-9ba8-1e66f868cdc7%2F42f97054-eaa7-431d-bf93-114a47a94c2d%2Fjxltmy_processed.png&w=3840&q=75)
Transcribed Image Text:**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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