Question

A company finds that if it charges x dollars for a cell phone, it can expect to sell 1,000−2x phones. The company uses the function r defined by r(x)=x⋅(1,000−2x) to model the expected revenue, in dollars, from selling cell phones at x dollars each. At what price should the company sell their phones to get the maximum revenue?

Answer 1

$500 will give the company the maximum revenue

Explanation:

Given

`r(x) = x (1000 - 2x)`

Required

Price to generate maximum revenue

We have:

`r(x) = x (1000 - 2x)`

Open bracket

`r(x) = 1000x - 2x^2`

Rewrite as:

`r(x) = - 2x^2 + 1000x`

The maximum value of x is calculated using:

`x = -(b)/(2a)`

Where:

`f(x) = ax^2 + bx + c`

So:

`a \to -2`

`b = 1000`

`c = 0`

`x = -(b)/(2a)`

`x = -(1000)/(-2)`

`x = (1000)/(2)`

`x = 500`