Question

Mathew 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= -3p^2 + 60p +1060, where p is the price of the company’s product. What should he use to determine the price of maximum sales?

Answer 1

Answer: The price of maximum sales is $160

Step-by-step explanation:

This question requires you to find the vertex of this equation. The vertex of a parabola is the point where the parabola crosses its axis of symmetry.

since the coefficient of the $x^2$ term is negative, the vertex will be the highest point on the graph.

this quadratic equation is in standard form: $y = ax^2+bx+c$.

From this, we can derive:

$a = -3$

$b = 60$

$c = 1060$

First, determine the axis of symmetry ($p$ is the variable for the horizontal axis ($x$) in this instance). This will be our x-coordinate of the vertex.

$p = \frac{-b}{2a}$

$p = \frac{-(60)}{2(-3)}$

$p = \frac{-60}{-6}$

$p=10$

Then, substitute the axis of symmetry into the function to find the y coordinate of the axis of symmetry. r stands for the variable for the vertical axis in this instance. This will be our y-coordinate of the vertex.

$r = -3(10)^2+60(10)+1060$

$r = 160$

As we have determined both the x and y coordinate of the vertex for this equation, we can determine that the maximum point is at $(10, 160)$.

the maximum price ($r$) is 160