Question
Asked Oct 21, 2019
An office wants to create a cubicle for a new employee. The cubicle will be rectangular​ , with three sides enclosed by cubicle wall and the fourth side open. What is the area of the largest possible cubicle that can be built if the office has 75
feet of cubicle​ wall?

 

check_circleExpert Solution
Step 1

The problem can be pictorially depicted as below. The perimeter available is 2x+y.

According to given data,

WALL
X
X
Y
2x+y 75
PERIMETER:
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WALL X X Y 2x+y 75 PERIMETER:

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Step 2

We have to maximize the area. So write an expression for area using the figure in step 1;

Area of the cubicle will be given by:
A = x-y
A x(75-2x)
A = 75x-2x2
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Area of the cubicle will be given by: A = x-y A x(75-2x) A = 75x-2x2

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Step 3

To maximize the area, take a derivative of area function with re...

d
d
75х - 2х?)
dx
(A)
dx
dA
d
(75x)-(2x2
dx
dx
dx
dA
75-4x
dx
dA
Set
0;
dx
75-4x 0
75
-= 18.75
4
х:
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d d 75х - 2х?) dx (A) dx dA d (75x)-(2x2 dx dx dx dA 75-4x dx dA Set 0; dx 75-4x 0 75 -= 18.75 4 х:

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Tagged in

Math

Calculus

Derivative