The break-even level of operation is represented by the point of intersection of two lines.
The break-even level of production means the profit is zero.

Consider the following graph.
The point (x
o
, y
o
) is referred to as the break-even point.
x
o
= break even quantity
y
o
= break even revenue
If x < x
o
then R(x) < C(x), therefore P(x) =R(x) –C(x) < 0 so you will have a loss.
If x > x
o
then R(x) > C(x), therefore P(x) = R(x) – C(x) > 0 so you will have a profit.

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Math 1313
Section 1.5
4
Example 5:
Find the break-even quantity and break-even revenue if C(x) = 110x + 40,000 and
R(x) = 150x.
Example 6:
The XYZ Company has a fixed cost of 20,000, a production cost of $12 for each unit
produced and a selling price of $20 for each unit produced.
a. Find the break-even point for the firm.
b. If the company produces and sells 2000 units, would they obtain a profit or loss?
c. If the company produces and sells 3000 units, would they obtain a profit or loss?

Math 1313
Section 1.5
5
Example 7:
Given the following profit function P(x) = 6x -12,000.
a. How many units should be produced in order to realize a profit of $9,000?
b. What is the profit or loss if 1,000 units are produced?
Example 8:
A bicycle manufacturer experiences fixed monthly costs of $124,992 and variable costs of
$52 per standard model bicycle produced. The bicycles sell for $100 each. How many bicycles must he
produce and sell each month to break even? What is his total revenue at the point where he breaks even?