Question

A model for a company's revenue is R = -12p2 + 240p + 10,000, where "p" is the price

in dollars of the company's product. Find the maximum revenue.

Answer 1

Maximum revenue is 11200 at price p=10.

Explanation:

If a quadratic function is defined by
`f(x)=ax^2+bx+c` and a<0, then it is maximum at
`((-b)/(2a),f((-b)/(2a)))`.

The revenue model of a company is

`R=-12p^2+240p+10,000`

Here,
`a=-12, b=240,c=10000`.

So,

`-(b)/(2a)=-(240)/(2(-12))=10`

It means, revenue is maximum at price 10.

Substitute p=10 in the revenue function.

`R=-12(10)^2+240(10)+10000`

`R=-1200+2400+10,000`

`R=11,200`

Therefore, maximum revenue is 11200 at price p=10.