Question

The profit made by a company when 60 units of its product is sold is $1600. When 150 units of its products are sold, the profit increases to $5200. Find the equation of the profit function assuming that the profit function is linear.

Answer 1

The profit function is linear so it can be written in the form

$P(u)=au+b$ (1)

where $P(u)$ is the profit depending on number of units $u$ , $a$ and $b$ are parameters that we have to find.

Substituting the condition that the profit made by a company when 60 units of its product is sold is $1600 to (1) we get the equation:

$1600=a∗60+b$ (2)

Substituting the condition that when 150 units of its products are sold, the profit increases to $5200 to (1) we get the equation:

$5200=a∗150+b$ (3)

Now we can find a and b from the system of equations (2),(3).

Lets subtract (2) from (3):

$5200−1600=a∗150+b−a∗60−b;$

$3600=a∗90;$

3600=a∗90;

$40=a;$

$a=40;$

Substituting $a=40$ we can find $b$ :

$1600=40∗60+b;$

$1600=2400+b;$

$−800=b;$

$b=−800;$

Substituting values of $a$ and $b$ to (1) we will get the function $P(u)=40u−800.$

Finally, the equation of the profit function is $P(u)=40u−800$, where $u$ is number of units.