How many mowers must be manufactured and sold each day for the company to break even?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:### Break-Even Analysis
Any manufacturing company has **costs** which include **fixed costs** such as plant overhead, product design, setup, and promotion; and **variable costs** that depend on the number of items produced. The **revenue** is the amount of money received from the sale of its product. The company **breaks even** if the revenue is equal to the cost.
![### Break-Even Analysis for a Small Plant Manufacturing Riding Mowers
A small plant manufactures riding mowers. The plant has fixed costs (leases, insurance, etc.) of $47,345 per day and variable costs (labor, materials, etc.) of $1,363 per mower produced. The mowers are sold for $1,910 each. The resulting cost and revenue equations are:
\[
\begin{array}{|c|c|}
\hline
y = 47,345 + 1,363x & \text{Cost equation} \\
\hline
y = 1,910x & \text{Revenue equation} \\
\hline
\end{array}
\]
where \( x \) is the total number of mowers produced and sold each day. The daily costs and revenue are in dollars.
Let's determine how many mowers must be manufactured and sold each day for the company to break even. At the break-even point, the cost and revenue are equal.
Set the cost equation equal to the revenue equation:
\[
47,345 + 1,363x = 1,910x
\]
Solve for \( x \):
\[
47,345 = 1,910x - 1,363x
\]
\[
47,345 = 547x
\]
\[
x = \frac{47,345}{547}
\]
\[
x \approx 87
\]
Therefore, the company must manufacture and sell approximately \(\boxed{87}\) mowers each day to break even. (Round to the nearest mower).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea6ddd78-5d51-4e2d-8762-122e3c25fe21%2F06cc2082-a67b-4b9a-afa2-b8827babefaa%2Ftn0z6vs_processed.png&w=3840&q=75)
Transcribed Image Text:### Break-Even Analysis for a Small Plant Manufacturing Riding Mowers
A small plant manufactures riding mowers. The plant has fixed costs (leases, insurance, etc.) of $47,345 per day and variable costs (labor, materials, etc.) of $1,363 per mower produced. The mowers are sold for $1,910 each. The resulting cost and revenue equations are:
\[
\begin{array}{|c|c|}
\hline
y = 47,345 + 1,363x & \text{Cost equation} \\
\hline
y = 1,910x & \text{Revenue equation} \\
\hline
\end{array}
\]
where \( x \) is the total number of mowers produced and sold each day. The daily costs and revenue are in dollars.
Let's determine how many mowers must be manufactured and sold each day for the company to break even. At the break-even point, the cost and revenue are equal.
Set the cost equation equal to the revenue equation:
\[
47,345 + 1,363x = 1,910x
\]
Solve for \( x \):
\[
47,345 = 1,910x - 1,363x
\]
\[
47,345 = 547x
\]
\[
x = \frac{47,345}{547}
\]
\[
x \approx 87
\]
Therefore, the company must manufacture and sell approximately \(\boxed{87}\) mowers each day to break even. (Round to the nearest mower).
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