Question

Matthew is a financial analyst for a surf board company He has found an equation for the revenue of selling t-shirts with the company logo to be r = -3p² +60p + 1060 where p is the price of the company's product What should he use to determine the price to maximize sales?

Answer 1

Solution

Step 1:

Write the revenue function

$\text{r = -3p}^2\text{ + 60p + 1060}$

Step 2:

The first derivative of the revenue should be used to determine the price to maximize sales.

$\begin{gathered} \text{r = -3p}^2\text{ + 60p + 1060} \\ \frac{dr}{dp}\text{ = -6p + 60} \\ -6p\text{ + 60 = 0} \\ 6p\text{ = 60} \\ p\text{ = }\frac{60}{6} \\ p\text{ = 10} \end{gathered}$