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July 30, 2014

July 30, 2014

Posted by **Jane** on Saturday, February 11, 2012 at 9:17am.

A cell phone company sells about 500 phones each week when it charges $75 per phone. It sells about 20 more phones per week for each $1 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?

- Math -
**Reiny**, Saturday, February 11, 2012 at 11:02amLet the number of $1 decreases be n

cost per phone = 75 - n

number sold = 500 + 20n

revenue = (500 + 20n)(75-n)

= 37500 + 1000n - 20n^2

using Calculus .....

d(revenue)/dn = 1000 - 40n = 0 for a max of revenue

40n=1000

n = 25

non-Calculus: completing the square ...

rev = -20(n^2 - 50n + 625-625)

= -20(n-25)^2 + 12500

max revenue is $12500 when n = 25

that is,

when the phone sells at $50

- Math -
**Reiny**, Saturday, February 11, 2012 at 11:20amLet the number of $1 decreases be n

cost per phone = 75 - n

number sold = 500 + 20n

revenue = (500 + 20n)(75-n)

= 37500 + 1000n - 20n^2

using Calculus .....

d(revenue)/dn = 1000 - 40n = 0 for a max of revenue

40n=1000

n = 25

non-Calculus: completing the square ...

rev = -20(n^2 - 50n + 625-625)

= -20(n-25)^2 + 12500

max revenue is $12500 when n = 25

that is,

when the phone sells at $50

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