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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 10cents for each seat above 50.

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




    My problem is that I am stuck on making a function from this word problem. I understand how to find the maximum profit, but without a function, I cannot do it! : (

    Anybody know the function to this problem?
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  2. #2
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    Quote Originally Posted by gearshifter View Post
    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 10cents for each seat above 50.

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

    ...
    The profit is calculated by:

    profit = (number\ of\ seats) \cdot (profit\ per\ seat)

    Let x denote the number of additional seats. Then the profit is:

    p(x)=(50+x)(6-0.1\cdot x)

    Expand the brackets and collect like terms:

    p(x)=-0.1\cdot x^2 + x +300

    ... and now it's your turn!

    (Only for the record: With 55 seats you'll get $3025)
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