# Maximizing Profit

• Apr 16th 2009, 04:13 PM
Shapeshift
Maximizing Profit
Here is the question:

A store sells portable MP3 players for \$100 each and, at this price, sells 120 MP3 players every month. The owner of the store wishes to increase his profit, and he estimates that, for every \$2 increase in the price of MP3 players, one less MP3 player will be sold each month. If each MP3 player costs the store \$70, at what price should the store sell the MP3 players to maximize profit?

I always have trouble figuring out what the function is.
Any help is appreciated.
• Apr 16th 2009, 04:45 PM
topher0805
Quote:

A store sells portable MP3 players for \$100 each and, at this price, sells 120 MP3 players every month. The owner of the store wishes to increase his profit, and he estimates that, for every \$2 increase in the price of MP3 players, one less MP3 player will be sold each month. If each MP3 player costs the store \$70, at what price should the store sell the MP3 players to maximize profit?
I'll help walk you through it.

• Apr 16th 2009, 04:57 PM
Shapeshift
x would represent the decrease in MP3 players
so if x were 1, one less MP3 player will be sold

2x would be the increase in price
so if x were 1, there would be a \$2 dollar increase

at least I think that makes sense (Thinking)
• Apr 16th 2009, 05:20 PM
skeeter
Quote:

Originally Posted by Shapeshift
Here is the question:

A store sells portable MP3 players for \$100 each and, at this price, sells 120 MP3 players every month. The owner of the store wishes to increase his profit, and he estimates that, for every \$2 increase in the price of MP3 players, one less MP3 player will be sold each month. If each MP3 player costs the store \$70, at what price should the store sell the MP3 players to maximize profit?

I always have trouble figuring out what the function is.
Any help is appreciated.

try this ...

let x = number of \$2 increases

price = (100 + 2x)

number sold = (120 - x)

cost = 70(120 - x)

can you proceed from here?
• Apr 16th 2009, 05:38 PM
Shapeshift
okay so in the end I got

x = 52.5

and I plugged that into the price function: (100 +2x)
and I get \$205