Constraint 1. V= 32000 cm³ xyz = 32000 g(x, y, z)=xyz-32000 vg = (y², xz, xy) function SA= xy + 2yz + 2xz f(x, y, z) = xy + 2yz + 2xz of = (y+2z₁ x +2=₁2₁+2x) y+2z = λ (yz) x-component x+2z=>(xz) y-component. 2y + 2x = x (xy) Z-Component xyz=32000 Constraint

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.8: Systems Of Linear Inequalities
Problem 2E
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A box without a lid is required to have volume, V = 32000 cm3. Minimize the
amount of cardboard required to create this box. Use the method of Lagrange Multipliers to solve this
problem.

Here's my work so far but now I'm stuck.

Constraint
1. V= 32000 cm³
xyz = 32000
g(x, y, z)=xyz - 32000
vg = (y²,₁ xz, xy)
function
SA= xy + 2yz + 2xz
ху
f(x, y, z) = xy + 2yz + 2xz
of = (y+az₁ x +2z₁ ay+ax)
y+2z = λ (yz)
x+2z = x (xz)
2y + 2x = x (xy)
xyz = 32000
x-component
y-component
Z-Component
Constraint
Transcribed Image Text:Constraint 1. V= 32000 cm³ xyz = 32000 g(x, y, z)=xyz - 32000 vg = (y²,₁ xz, xy) function SA= xy + 2yz + 2xz ху f(x, y, z) = xy + 2yz + 2xz of = (y+az₁ x +2z₁ ay+ax) y+2z = λ (yz) x+2z = x (xz) 2y + 2x = x (xy) xyz = 32000 x-component y-component Z-Component Constraint
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