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Math Help - Quadratic Optimization

  1. #1
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    Exclamation Quadratic Optimization

    Hey, everyone! I've been working on my homework and this one problem's got me confused. Can someone help me get started? (Sorry, I'm rather lousy at math.)

    A rectangle is bounded by the x-axis and the y-axis with a vertex on line p as shown below.


    a) Write a formula for the base of the rectangle in terms of x.
    b) Write a formula for the height of the rectangle in terms of x.
    (Hint: find the equation of line p.)
    c) Write a function for the area of the rectangle as a function of x.
    d) What bae and height should the rectangle have in order to produce the rectangle with the maximum area? Find its area.


    Really, I just need help setting up a and b. But any and all help is greatly appreciated!
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by miyosuke View Post
    Hey, everyone! I've been working on my homework and this one problem's got me confused. Can someone help me get started? (Sorry, I'm rather lousy at math.)

    A rectangle is bounded by the x-axis and the y-axis with a vertex on line p as shown below.


    a) Write a formula for the base of the rectangle in terms of x.
    b) Write a formula for the height of the rectangle in terms of x. (Hint: find the equation of line p.)
    c) Write a function for the area of the rectangle as a function of x.
    d) What bae and height should the rectangle have in order to produce the rectangle with the maximum area? Find its area.

    Really, I just need help setting up a and b. But any and all help is greatly appreciated!
    a) Base of the rectangle = x, where x is 0 \leq x \leq 40
    b) Height of the rectangle:
    equation of the line is given by y = mx + b \implies y = -\frac{1}{2}x + 20

    so ht of the rectangle is = -\frac{1}{2}x + 20, where 0 \leq x \leq 40
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  3. #3
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    Thanks kalagota, I managed to figure it out with your help. (Salamat, ha! )
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  4. #4
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by miyosuke View Post
    Thanks kalagota, I managed to figure it out with your help. (Salamat, ha! )
    ui!! pinoy blood?
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by kalagota View Post
    ui!! pinoy blood?
    Hey! I've got some pinoy blood in my refrigerator. It makes really good beef stock.

    -Dan
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  6. #6
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    Quote Originally Posted by kalagota View Post
    ui!! pinoy blood?
    Opo.

    Topsquark: Eep!
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  7. #7
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by miyosuke View Post
    Opo.

    Topsquark: Eep!
    naka-base ka sa US? wow!!
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