Question

Suppose you have 48 feet of fencing to enclose a rectangular dog pen. The function A=24x-x^2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area?

Answer 1

Width: 12 ft

Maximum area: 144 ft²

Explanation:

A = 24x – x²

A = –x² + 24x

A = –(x² – 24x)

A = –(x² – 24x + 144) + 144

A = –(x – 12)² + 144

Therefore, the maximum area of 144 ft² occurs at x = 12 ft.