Question

Find absolute extrema on closed regions (using the u’s)?

A shipping company handles rectangular boxes provided the sum of the height and the girth does not exceed 96 inches. ( Girth is the perimeter of the base). Find the dimensions of the box of largest volume that the company will ship.

This is my work. Let me know if i did it right or if not, what i did wrong. Thanks a lot for your help!!!

http://postimg.org/image/k01vjiizt/

http://postimg.org/image/uw2autt0t/

http://postimg.org/image/v1mu3of5f/

Answer 1

calculus or algebra?

Answer 2

calculus 3 please

Answer 3

2l + 2w + h <= 96 is our constraint

Legrande multipliers?

Answer 4

flipping back and forth between the pictures gets me a bit lost in the process. these old eyes arent what they used to be :)

Answer 5

I think so yeah. I forgot the fancy words of terminology haha. It is finding absolute extrema on closed regions (using the u’s)

Answer 6

V = lwh

Vl = wh; Cl = 2n
Vw = lh; Cw = 2n
Vh = lw; Ch = n

wh = 2n = lh when w=l, and n=l^2

h=2n/l = 2l

6 l^3 <= 96

l = cbrt(96/6)

V = 2*96/6 = 32

is what im getting to

Answer 7

did you get 32 as well?

Answer 8

i got that my dimensions were (16,16,32)

Answer 9

http://www.wolframalpha.com/input/?i=maximize+xyz+given+that+2x%2B2y%2Bz%3C%3D+96

the wolf agrees

Answer 10

16,16,32 should maximize the volume yes

Answer 11

you could do that in wolf? wow

Answer 12

but i dont get your process

Answer 13

how could you do in such a short space what i spent 3 papers doing? explain please

Answer 14

@pooja195

@Mehek14

Answer 15

@amistre64

Answer 16

me? years of making mistakes have allowed me to simply avoid the steps that i keep messing up on lol

Answer 17

but did you check my process? Because it is a take home test the professor would take points off for nothing.

Answer 18

@Hero

Answer 19

i tried to follow the pictures you posted, but i cant keep track of them.

Answer 20

i cant say i know what "the u's" refers to so the method may not be my thing

Answer 21

Do you understand the concept @blackstreet23 ?

Answer 22

i guess i do, but i think i might make some mistake in the process. I think i know i got the right answer, but i want to make sure, i just didnt get it for the wrong reasons

Answer 23

@texaschic101

Answer 24

let me find someone who can clear this up

@Luigi0210 @amistre64 @sleepyhead314 @sleepyjess

Answer 25

Thanks for that :)

Answer 26

@pooja195

Answer 27

@IrishBoy123 @surjithayer

Answer 28

If you still dont understand the concept and would like a refund, then just tell me and i will be willing to give you, your refund :D

Answer 29

Yes I guess that is the best. I would like the refund

Answer 30

I apologize for not receiving great help D:

You will be given your Ob's Back :D

Answer 31

hey yeah. I never got them back :(