Question

The point at which a company's costs equal its revenues is the break-even point, C represents the production cost, in dollars, of x units of a product and $R$ represents the revenue, in dollars, from the sale of $x$ units. Find the number of units that must be produced and sold in order to break even. That is, find the value of $x$ for which $C=R$ $$\begin{aligned} &C=3 x+400\\ &R=7 x-600 \end{aligned}$$

Name: Problem 74, Chapter 9: Algebra and Trigonometry
Uploaded: 2020-07-05T11:24:01-08:00
Duration: 50 s
Channel: Ankit Gupta
Description: The point at which a company's costs equal its revenues is the break-even point, C represents the production cost, in dollars, of x units of a product and R represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold in order to break even. That is, find the value of x for which C=R C=3 x+400 R=7 x-600

   The point at which a company's costs equal its revenues is the break-even point, C represents the production cost, in dollars, of x units of a product and $R$ represents the revenue, in dollars, from the sale of $x$ units. Find the number of units that must be produced and sold in order to break even. That is, find
the value of $x$ for which $C=R$
$$\begin{aligned}
&C=3 x+400\\
&R=7 x-600
\end{aligned}$$

Algebra and Trigonometry

Judith A. Beecher,… 4th Edition

Chapter 9, Problem 74

Instant Answer

Solved by Expert Ankit Gupta

07/05/2020

Step 1

We are asked to find the break-even point, which is the point where $C=R$. Show more…

Show all steps

Thanks for your feedback!

The point at which a company's costs equal its revenues is the break-even point, C represents the production cost, in dollars, of x units of a product and $R$ represents the revenue, in dollars, from the sale of $x$ units. Find the number of units that must be produced and sold in order to break even. That is, find the value of $x$ for which $C=R$ $$\begin{aligned} &C=3 x+400\\ &R=7 x-600 \end{aligned}$$

Play audio

Feedback

Ankit Gupta and 76 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Break-even Analysis

Break-even analysis involves determining the point at which total costs equal total revenues. This concept is critical in business and economics because it helps in understanding when a product or venture will start to generate profit, providing a clear indication of the minimum production and sales levels required for financial sustainability.

Linear Equations

Linear equations are fundamental algebraic expressions where the variables exhibit a constant rate of change, typically represented in a form such as ax + b = cx + d. In the context of break-even analysis, linear equations model the relationship between cost and revenue. Solving these equations enables one to determine the precise quantity at which expenses and earnings are balanced.

Please give Ace some feedback