Question

HELLP ASAP

A bicycle manufacturer uses the given expression to model the monthly profit from sales of a new model of bicycle, where x is the selling price of one bicycle, in dollars.


-x^2 + 300x -20,000


At what selling prices for the bicycle will the manufacturer make neither a profit nor a loss?


$100

$150

$200

$50

$250

$300

Answer 1

$100 and $200

Explanation:

The profit equation is:

`f(x)=-x^(2)+300x-20000`

The manufacturer will make no profit nor a loss when the profit is equal to zero. So setting the profit equation equal to zero will give us the price(x) of bicycles at which there is no profit no loss condition.

`-x^(2)+300x-20000=0\\\\ x^(2)-300x+20000=0\\\\ x^(2)-200x-100x+20000=0\\\\ x(x-200)-100(x-200)=0\\\\ (x-100)(x-200)=0\\\\ x = 100, x = 200`

This means when the price of bicycles sold is either 100 or 200 the manufacturer makes no profit.