Question

A bi-monthly sports magazine has 48,000 subscribers when it charges $20 for a one year subscription. For every $1 increase in the yearly subscription price, the magazine assumes that it will lose 2,000 subscribers resulting in the equation below. Using the equation below, how much should the magazine sell for in order to maximize revenues? f (x) = (48,000 – 2,000x) (20 + x)​

Answer 1

To maximize the profits of the company, the subscription price should be raised to $ 22.

Explanation:

Given that a bi-monthly sports magazine has 48,000 subscribers when it charges $ 20 for a one year subscription, and for every $ 1 increase in the yearly subscription price, the magazine assumes that it will lose 2,000 subscribers resulting in the equation below, to determine, Using the equation below, how much should the magazine sell for in order to maximize revenues, the following calculations should be performed:

f (x) = (48,000 - 2,000x) (20 + x)

X = 48,000 x 20 = 960,000

X = (48,000 - 2,000x1) x (20 + 1)

X = 46,000 x 21

X = 966,000

X = (48,000 - 2,000x2) x (20 + 2)

X = 44,000 x 22

X = 968,000

X = (48,000 - 2,000x4) x (20 + 4)

X = 40,000 x 24

X = 960,000

Therefore, to maximize the profits of the company, the subscription price should be raised to $ 22.