# Math Help - Applied optimization in calculus

1. ## 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?

2. Originally Posted by yoman360
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.