Question

A company can sell 2000 magazine subscriptions at $40 each. For each $5 increase in the price, it will sell 200 fewer subscriptions.

What subscription price will provide the maximum revenue for the company?

a) $55 b) $40 c) $45 d) $50

Answer 1

$45 is the price that provide the maximum revenue

Explanation:

Let x be the number of times the price increase

A company can sell 2000 magazine subscriptions , for each price increase they sell 200 few subscriptions. (2000-200x) for x times increase.

for each $5 increase, the cost becomes 40+5

For x times increase the cost becomes 40+5x

Revenue is cost time the number of magazines

`R(x)= (2000-200x)(40+5x)`

`R(x)=-1000x^2+2000x+80000`

`R(x)=-1x^2+2x+80`

a=-1 and b = 2

To get maximum revenue find out the vertex

`x=(-b)/(2a) =(2)/(2(-1)) =1`

price is 40+5x= 40+5(1)= 45

so $45 is the price that provide the maximum revenue