Thread: 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?

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:

where .

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