Question

6. MobiStar is a mobile services company that sells 800 phones each week

when it charges $80 per phone. It sells 40 more phones per week for each
$2 decrease in price. The company's revenue is the product of the
number of phones sold and the price of each phone. What price should
the company charge to maximize its revenue?
Part A: Let d represent the number of $2 decreases in price. Letr be the
company's revenue. Write a quadratic function that reflects the
company's revenue.
Hint: The number of phones sold will be 800 + 40d since they sell 40 more
phones for every $2 decrease. The price for the phones will be 80 - 2d
since d is the number of decreases and each decrease is $2.​

Answer 1

$60

Step-by-step explanation:

Let d represent the number of $2 decreases in price and Let r be the

company's revenue.

The price of the phone (P) for d number of price decrease = 80 - 2d

The number of phones sold as a result of d number of price decrease = 800 + 40d

The revenue (r) = price of phone * number of phone sold

r = (80 - 2d)(800 + 40d)

Multiplying the bracket:

r = 64000 + 3200d - 1600d - 80d²

r = 64000 + 1600d - 80d²

The maximum revenue is at r' = 0. Hence:

r' = 1600 - 160d

0 = 1600 - 160d

160d = 1600

d = 1600 / 160

d = 10

The price at maximum revenue = 80 - 2d = 80 - 2(10) = 80 - 20

Price = $60