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Math Help - Please Help With This Problem

  1. #1
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    Please Help With This Problem

    A baseball card store can obtain sports cards at a cost of $5 per card, and has been selling them at a rate of 50 cards per month for a price of $9. The store is planning to change the card price, and estimates that for each $0.50 per card reduction, 10 more cards will be sold each month. At what price per card will the store owner maximize his/her profit? I need to find the answer using calculus and I'm not sure how to solve it using calculus. If you could help me out I would appreciate it.
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  2. #2
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    Quote Originally Posted by The Math Man View Post
    A baseball card store can obtain sports cards at a cost of $5 per card, and has been selling them at a rate of 50 cards per month for a price of $9. The store is planning to change the card price, and estimates that for each $0.50 per card reduction, 10 more cards will be sold each month. At what price per card will the store owner maximize his/her profit? I need to find the answer using calculus and I'm not sure how to solve it using calculus. If you could help me out I would appreciate it.
    let x = number of 50 cent reductions

    revenue = (number of cards sold)(price per card)

    R(x) = (50 + 10x)(9 - .5x)

    cost function = (cost per card)(number of cards sold)

    C(x) = 5(50 + 10x)

    profit = revenue - cost

    P(x) = (50 + 10x)(9 - .5x) - 5(50 + 10x) = (50 + 10x)(4 - .5x)

    find the maximum profit using the method taught to you in class
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