You are assigned a task to a rectangular cubicle with four w

You are assigned a task to a rectangular cubicle with four walls. The cubicle will be designed as in the following diagram, where the wall on the top of the diagram is exactly half as long as the wall on the bottom of the diagram. A door will be placed for the other half of the wall in order to enclose the cubicle, but no wall will be used there. If you have 260 feet of cubicle wall, what is the largest you can make the area of the cubicle? The largest area is 5633.33 square feet. If necessary, round to two decimal places.

Solution

Let length of wall be x and width be y

So, Total length of cubicle wall:

x+ x/2 + y +y = 260

3x/2 +2y = 260 ---(1)

y = 130 - 3x/4

Area = x*y = x( -3x/4 +130)

= -3x^2/4 + 130x

Maximum are would occur at vertex : x = -b/2a = -( 130/(-2*3/4))

= 130/3/2 = 260/3 = 86.67 ft

Maximum Area = -3(86.67)^2/4 + 130*86.67

= 5633.33 sq feet