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8 January, 18:09

Silver scooter finds that it costs $300 to produce each scooter and the fixed costs are $750. The price is given by p=900-x, where p is the price in dollars at which exactly x scooters will be sold. Find the quantity of scooters that the company should produce and the price it should charge to maximize profit. Find the maximum profit ...?

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  1. 8 January, 19:40
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    Cost = 300 x + 750, where x is the number of the scooters;

    Price = 900 - x

    Profit = x (900 - x) - (300 x + 750) =

    = 900 x - x² - 300 x - 750 = - x² + 600 x - 750

    d (Profit) = - 2 x + 600

    - 2 x + 600 = 0

    x = 600 : 2

    x = 300

    The company must produce 300 scooters to maximize the profit.

    The maximum profit is:

    - 300² + 600 · 300 - 750 = $89,250
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