Question

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells small radios. More than how many radios must be produced and sold for the company to have a​ profit?

The company must produce and sell more than ? radios to have a profit.

Answer 1

ANSWER

The company must produce and sell more than 700 radios to have a profit.

EXPLANATION

The revenue function is

$R(x)=40x$
and the cost function is

$C(x)=5,600+32x$


The company will break even when total revenue is equal to the total cost.


This implies that,


$40x =5,600+32x$

We group similar terms to get,


$40x - 32x = 5600$

This simplifies to,

$8x = 5600$

Divide both sides by 8 to get,


$x = \frac{5600}{8}$


$x = 700$


The company breaks even by producing and selling 700 radios.

The company must produce and sell more than 700 radios to have a profit.