Question

A sales team estimates that the number of new phones they will sell is a function of the price that they set. They estimate that if they set the price at x dollars, they will sell f(x)=4564−7x phones. Therefore, the company's revenue is x⋅(4564−7x). Find the price, x, which will maximize the company's revenue.

Answer 1

Answer:

$2282  

Step-by-step explanation:

ƒ(x) = x(4564-x) = 4564x - x²

In standard form,

ƒ(x) = -x² + 4564x

a = -1; b = 4564; c = 0

This is the equation of an inverted parabola, because a < 0. Therefore, the vertex is a maximum.

The vertex of a parabola occurs at

x = -b/(2a) = -4564/[-2 × (-1)] = -4564/(-2) = 2282.

The price that will maximize the company's revenue is $2282.

The graph below shows that the company's maximum revenue is over $5.2 million.