(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

i needed to find the max and min possible volume for a box with edges that = 200cm and surface area that = 1500cm^2 using Lagrange multipliers.

2. Relevant equations

edges: 4x + 4y + 4z = 200cm

Area: 2xy + 2xz + 2yz = 1500 cm^2

Volume = xyz

3. The attempt at a solution

i brought it down to this:

Vol = f

Area = G

Edges = g

^f = ^G# + ^g$

(# and & just means 'some number')

( ^ is the gradient of the function)

when i simplify everything out i get these statements:

yz = #(y + z) + $

xz = #(x + z) + $

xy = #(x + y) + $

x + y +z = 50

xy + yz + yz = 750

when i try to replace values it seems to get messy. do i just throw in random values for # and $ or something? im 99% sure that they cannot = 0. that is pretty much all i can say from these statements right now lol

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# Homework Help: LaGrange max/min (calc 3)

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