Applied Mathematics for Business and Economics

Lecture Note Function

Example 3
The Green-Belt Company determines that the cost of manufacturing men’s belts is $ 2
each plus $ 300 per day in fixed costs. The company sells the belts for $ 3 each. What
is the break-even point?
Solution
The break-even point occurs where revenue and cost are equal. By letting x = the
number of belts manufactured in a day, and then we obtain revenue funcion

R()x= 3 xand cost functionCx()=+ 230 x 0. ForCx Rx( )= ( ), we obtain

3230

300

xx

x

= + 0

=

So, 300 belts must be sold each day for the company to break even. The company
must sell more than 300 belts each day to make a profit.

Example 4
Suppose that a company has determined that the cost of producing x items is
500 + 140x and that the price it should charge for one item is P = 200 – x
a. Find the cost function.
b. Find the revenue function.
c. Find the profit function.
d. Find the break-even point
Solution
a. The cost function is given:Cx( )=+500 140x

Y

300 -

200 -

100 -

......
0 100 200 300 400 500 600 X

1000 -

900 -

800 -

700 -

600 -

500 -

400 -

Profit

C(x) = 2x + 300

Break-even point

Loss

R(x) = 3x

•

Loss

Profit

0

y

x

Revenue: yRx= ( )

Cost: yCx= ( )

P

Break-even point