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?

We are given

where

x is width of rectangle

A is area of rectangle

Since, we have to maximize it

so, we will find it's derivative

and then we can set it to 0

and then we can solve for x

now, we can set it to 0

and then we can solve for x

So, width is 12  feet

Maximum area:

we can plug x=12

So, the maximum area is

................Answer

$450

step-by-step explanation:

first, you have to multiply 150x2=300

next, you have to add 150+300= 450

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2