Question

9)

Select Audio Company sells an MP3 player for $75. At that price, the company sell
approximately 1000 players per week. The company predicts that for every $5 increase in
price, it will sell 50 fewer MP3 players. Write an equation to represent the revenue with where
represents the number of price increases. Which price for an MP3 player will maximize the
revenue?

Answer 1

The equation to represent the revenue is f(x) = -250x² + 1250x + 75000

The price that will maximize revenu is $2.50

Write an equation to represent the revenue

From the question, we have the following parameters that can be used in our computation:

Price = $75 per MP3 player

Sales per week = 1000

Also, we have

for every $5 increase in price, it will sell 50 fewer MP3 players.

So, we have the equation to be

f(x) = (75 + 5x)(1000 - 50x)

Expand

f(x) = -250x² + 1250x + 75000

The priice of MP3 at the maximum profit is

x = -b/2a

x = -1250/(2 * -250)

x = 2.5

So, we have

f(2.5) = -250 * 2.5² + 1250 * 2.5 + 75000

Evaluate

f(2.5) = 76562.5

Hence, the price that will maximize profit is $2.50