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Math Help - Applications of Extrema

  1. #1
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    Applications of Extrema

    In planning a restaurant, it is estimated that a profit of $6 per seat will be made if the number of seats is no more than 50, inclusive. On the other hand, the profit on each seat will decrease by 10 cents for each seat above 50.
    a) Find the number of seats that will produce the maximum profit.

    Okay.. I know HOW to do it, I just don't know how to set up the equation. Help?

    Is it like this?
    P=6x-0.1(50+x)

    I know Profit = Revenue - Cost, but do we need to use that here?
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  2. #2
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    Hello, Jiyongie!

    Your function is off . . . but you were close.


    In planning a restaurant, it is estimated that a profit of $6 per seat will be made
    if the number of seats is no more than 50, inclusive.
    On the other hand, the profit on each seat will decrease by 10 for each seat above 50.

    a) Find the number of seats that will produce the maximum profit.

    Let x = number of seats in excess of 50.

    There will be: . 50 + x seats.

    Then each seat brings a profit of: . 6 - 0.1x dollars.


    Therefore: . P \;=\;(6-0.1x)(50+x)

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