Question

Could someone please help me finish this Lagrange Multiplier problem ( http://f.imgtmp.com/GMPs2.jpg )? Here is my work so far: http://f.imgtmp.com/Jeijx.jpg .

Answer 1

do you have to lagrange it?

Answer 2

No.

Answer 3

8=lwh; h=8/lw

Sa = 10lw + 32/w + 80/l

Sa' = 10l'w + 10lw' -32w'/w^2 -80l'/l^2

is my first thought

Answer 4

it might be easier with a lagrange, but i havent done them in so long that i forgot some of the more important parts :)

Answer 5

Sa = 10lw + 32lh + 80wh - L(lwh-8)

Sal = 10w +32h -L(wh)
Saw = 10l +80h -L(lh)
Sah = 32l +80w -L(lw)
SaL = 8+lwh

those should play apart

Answer 6

the Sa:lwh parts are spose to zero out i believe

Sal = 10w +32h -L(wh) = 0
L = 10/h + 32/w

Saw = 10l +80h -L(lh) = 0
L = 10/h + 80/l

Sah = 32l +80w -L(lw) = 0
L = 32/w + 80/l

Answer 7

L = 10/h + 32/w
-L = -10/h - 80/l
-----------------
0 = (32l - 80w)/lw


L = 10/h + 80/l
-L = -32/w - 80/l
----------------
0 = (10w-32h)/hw


w = 4l
w = 32h
-----------
4l = 32h; l=8h

l = 8h
w=32h
h=h

256h^3 - 8 = 0

h = cbrt(8/256)

maybe

Answer 8

i missed it someplace, im sure

Answer 9

h = (8/256)^(1/3) is not the answer for (a), (b), or (c) :(.