Question

Find the dimensions of the regular corral split into 2 pens of the same size producing the greatest possible enclosed area given 900 feet of fencing.

Answer 1

Length = 225 ft

Width = 150 ft

Explanation:

If L is the length and W is the width, then:

900 = 2L + 3W

A = LW

Solve for W in the first equation:

3W = 900 − 2L

W = 300 − ⅔ L

Substitute into the area equation:

A = L (300 − ⅔ L)

A = 300L − ⅔ L²

Use calculus to find dA/dL and set to 0, or use the formula for vertex of a parabola.

Using calculus:

dA/dL = 300 − 4/3 L

0 = 300 − 4/3 L

L = 225

Using vertex formula:

L = -b / (2a)

L = -300 / (-4/3)

L = 225

Find the width:

W = 300 − ⅔ L

W = 150

You got the right answers, but the problem says to assume that the length is greater than the width.