Question

You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=64. Find the dimensions which minimize the surface area of this box.

Answer 1

Looks like a Lagrange multiplier problem

Answer 2

so what will i have to do?

Answer 3

\[\nabla f=\lambda \nabla g\]

where \[f(x,y,z)=2xy+2xz+2yz\]
and \[g(x,y,z)=xyz-64\]

Answer 4

zarkon is there anyway of contacting u other than openstudy

Answer 5

why?

Answer 6

i feel like u can usually help me with contest questions

Answer 7

its cool if u dont want to be bothered

Answer 8

ic...and I'm not on OS enough :)

Answer 9

oh lol kk, @ what times do u usally come to openstudy....just wanna know when i can catch u

Answer 10

I get e-mail notification when someone replies to a thread that I have replied to.

so you could find one of my posts and reply to it. I will then get an email.

Answer 11

ok

Answer 12

how did u get the f(x,y,z)=2xy+2xz+2yz ?

Answer 13

if the dimensions are x,y,z then the surface area is just the sum of the areas of the 6 sides

xy+xy+xz+xz+yz+yz=2xy+2xz+2yz

Answer 14

ok i been trying to solve this but i can not this is what i have so far\[fx=2y+2z=\lambda(yz)
fy= 2x+2z=\lambda(xz)
fz= 2x+2y=\lambda(xy) \]

Answer 15

ok so far

Answer 16

do this...

multiply the first one by x and the 2nd one by y to get

\[2xy+2xz=\lambda xyz\] and \[2xy+2yz=\lambda xyz\]

so

\[2xy+2xz=2xy+2yz\]

\[\[2xz=2yz\]

\[x=y\]

Answer 17

ok and we do the same for z right?

Answer 18

i got z= y

Answer 19

yes

Answer 20

so how will i get the value of any of them?

Answer 21

v=64 should i 64/3?

Answer 22

x=y=z so x*y*z=64 turns into

\[x^3=64\]

x=4

Answer 23

ooo k

Answer 24

thanx a lot of your help

Answer 25

np