Question

Suppose you have 48 feet of fencing to enclose a rectangular dog pen. The function

A = 24x-x2, 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

we are given

`A=24x-x^2`

where

A is area of rectangle

x is width of rectangle

Since, we have to maximize area

so, we will find derivative

`A'=24* 1-2x`

`A'=24-2x`

now, we can set it to 0

and then we can solve for x

`A'=24-2x=0`

`24-2x=0`

`x=12`

The width which gives you the maximum area is 12 feet........Answer

now, we can plug x=12 to find area

`A=24(12)-(12)^2`

`A=288-144`

`A=144ft^2`

So, the maximum area is

`A=144ft^2`............Answer