Homework Help is Here – Start Your Trial Now!
Math
Statistics
How many mowers must be manufactured and sold each day for the company to break even?

How many mowers must be manufactured and sold each day for the company to break even?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

L3

### 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.
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).
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).
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS