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Math Help - Maximizing Profit

  1. #1
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    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.
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  2. #2
    Senior Member topher0805's Avatar
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    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.

    First identify your variables.
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  3. #3
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    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
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  4. #4
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    Quote Originally Posted by Shapeshift View Post
    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?
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  5. #5
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    okay so in the end I got

    x = 52.5

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