Question
Asked Oct 22, 2019
An open rectangular box is 22feet long and has a surface area of
96 square feet. Find the dimensions of the box for which the volume is as large as possible.
 
check_circleExpert Solution
Step 1

Given, length of box is 22 feet and surface area are 96 square feet.

V lbh
S lb+2bh+21h
where, lngth b= breadth h = height
....1)
V 22bh
S 22b+ 2bh+2(22) h
S 22b 2bh44h 96
-(2)
help_outline

Image Transcriptionclose

V lbh S lb+2bh+21h where, lngth b= breadth h = height ....1) V 22bh S 22b+ 2bh+2(22) h S 22b 2bh44h 96 -(2)

fullscreen
Step 2

Apply Lagrange Multiplier,

H = V -AS
,2-multiplier constant
H 22bh- 2(22b+ 44h+2bh-95)
help_outline

Image Transcriptionclose

H = V -AS ,2-multiplier constant H 22bh- 2(22b+ 44h+2bh-95)

fullscreen
Step 3

Differentiate above with respect to b...

H, 22h-2(22+2h)
H 22b-2(44+2b)
H(22b44h2bh-95)
help_outline

Image Transcriptionclose

H, 22h-2(22+2h) H 22b-2(44+2b) H(22b44h2bh-95)

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour*

See Solution
*Response times may vary by subject and question
Tagged in

Math

Calculus

Derivative