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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- Sep 23rd 2009, 09:50 PMyoman360Applied 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? - Sep 23rd 2009, 10:00 PMmr fantastic
Draw a diagram. Let the width of the

**area**be 2x (the factor of 2 is for convenience) and the length be y. Then:

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

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