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Thread: Calculus economics problem

  1. #1
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    Calculus economics problem

    The bigger battery company sells car batteries at $60 each. They give a discount of 36n, cents per battery, where n is the number of batteries purchased. Find the number of batteries the company should persuade Marky's Car Repairs to purchase in order to make the greatest income.

    Answer:83

    Not sure how to solve this problem
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  2. #2
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    Re: Calculus economics problem

    Quote Originally Posted by kguelly View Post
    The bigger battery company sells car batteries at $60 each. They give a discount of 36n, cents per battery, where n is the number of batteries purchased. Find the number of batteries the company should persuade Marky's Car Repairs to purchase in order to make the greatest income.
    Answer:83
    Not sure how to solve this problem
    Revenue $R(n)=[60-0.36n]*n=60n-0.36n^2$ Find maximum revenue: $R'(n)=0$
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  3. #3
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    Re: Calculus economics problem

    Quote Originally Posted by kguelly View Post
    The bigger battery company sells car batteries at $60 each. They give a discount of 36n, cents per battery, where n is the number of batteries purchased.
    So if you buy n batteries, you will be charged 60- .36n per battery so a total or n(60- 0.36n)= 60n- 0.36n^2 dollars.

    Find the number of batteries the company should persuade Marky's Car Repairs to purchase in order to make the greatest income.

    Answer:83

    Not sure how to solve this problem
    You can either, as Plato suggested, set the derivative equal to 0 or, since this is quadratic, complete the square to find the vertex of the parabola.
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