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Math Help - Applied optimization in calculus

  1. #1
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    Applied optimization in calculus

    suppose that 600ft of fencing are used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle. Find the dimensions of the corral with maximum area.

    this is really confusing and Whats a corral?
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  2. #2
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    Quote Originally Posted by yoman360 View Post
    suppose that 600ft of fencing are used to enclose an area in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle. Find the dimensions of the corral with maximum area.

    this is really confusing and Whats a corral?
    Draw a diagram. Let the width of the area be 2x (the factor of 2 is for convenience) and the length be y. Then:

    A = 2xy + \frac{\pi x^2}{2} where 600 = 2x + 2y + \pi x.

    Re-write A in terms of x alone and use calculus in the usual way.
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