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Math Help - Is this Optimization function right?

  1. #1
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    Is this Optimization function right?


    A real estate developer is contemplating the construction of a luxury condominium building.
    Profit per unit is expected to be $200,000 if 20 units are built, but will decrease by $4000 for
    each additional unit built on the site. How many units should be built in order to maximize

    total profit?

    For some reason i find these problems very tricky. So, is this function right for profit?:

    Price per unit = 200000 - ((x-20) 4000)

    Profit = x(200000 - ((x-20) 4000))

    Thanks!
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  2. #2
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    Quote Originally Posted by Arturo_026 View Post
    A real estate developer is contemplating the construction of a luxury condominium building.
    Profit per unit is expected to be $200,000 if 20 units are built, but will decrease by $4000 for
    each additional unit built on the site. How many units should be built in order to maximize
    total profit?

    For some reason i find these problems very tricky. So, is this function right for profit?:

    Price per unit = 200000 - ((x-20) 4000)

    Profit = x(200000 - ((x-20) 4000))

    Thanks!
    Let N be the number of units more than 20 so

     <br />
N = 20 + x<br />

    The profit decreases $4000 per unit so

     <br />
P = 200,000 - 4000 x<br /> <br />

    Total profit

     <br />
PN = (x+20)(200,000-4000x).<br />

    It's this you want to maximize.
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  3. #3
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    Quote Originally Posted by Danny View Post

    The profit decreases $4000 per unit so

     <br />
P = 200,000 - 4000 x<br /> <br />
    This is what I don't get. The problem says that the price decreases for additional units. So, when 20 units are built the profit is 200,000 and when it's 21, the profit is 196,000. So shouldn't the profit per unit be
    <br />
200,000 - 4,000 (20-x)<br />
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  4. #4
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    Quote Originally Posted by Arturo_026 View Post
    This is what I don't get. The problem says that the price decreases for additional units. So, when 20 units are built the profit is 200,000 and when it's 21, the profit is 196,000. So shouldn't the profit per unit be
    <br />
200,000 - 4,000 (20-x)<br />
    My numbers are more than 20 whereas yours are starting a zero although if you put in 21 into your formula it gives 204,000 instead of 196,000.
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  5. #5
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    Quote Originally Posted by Danny View Post
    My numbers are more than 20 whereas yours are starting a zero although if you put in 21 into your formula it gives 204,000 instead of 196,000.
    Yes, I meant x-20.
    Ok I see, thanks.
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