Question

mrs.riches can sell 36 picture frames each month if she charges $12 each. she estimates that for each $4 increase in price, she will sell 4 fewer frames. what will be the maximum revenue?

Answer 1

The following table shows the behavior of sales for some values:

We can find the revenue for x frames with the following function:

`r(x)=x(48-x)`

Where 48-x represents the price. By multiplying we have:

`r(x)=-x^2+48x`

What is a parabola that opens downwards, and the point that is higher (vertex) will give us the maximum revenue.

To find the maximum value we can find the derivative and set it equal to 0:

`r´(x)=-2x+48`
`0=-2x+48`

`2x=48`

`x=(48)/(2)`
`x=24`

As we saw with the table and the function, the highest revenue is reached by selling 24 marks at 24 dollars, which gives us 576 dollars.