Need help finding constraint

Question

astrophysics · Answer

Question: A rectangular box with no top and two intersecting partitions is to be constructed from 192 square inches of cardboard (see the figure below). Find the dimensions that will maximize the volume. [Langrange Multiplier] http://puu.sh/ddNlS/0d0bb4c334.png image of the box

astrophysics · Answer

S = 3zx+3zy+xy - 192 = 0?

astrophysics · Answer

I keep thinking it's a square box lol

astrophysics · Answer

Letting z = height, z = width, y = length I suppose

astrophysics · Answer

x = width*

ganeshie8 · Answer

maximize f(x,y,z) = xyz
subject to  3zx+3zy+xy = 192 

?

astrophysics · Answer

Yeah, I'm just making sure I had the surface area right :P

ganeshie8 · Answer

u want me check the expression?

ganeshie8 · Answer

Looks good!
you have 3 vertical sides and 3 horizontal sides

astrophysics · Answer

$$f(x,y,z, \lambda) = x \times y \times z + \lambda (3zx+3zy+xy-192)$$ this is all I wanted you to make sure, I can do the rest :P

astrophysics · Answer

Cool, thanks ^.^, really getting the hang of this stuff, it's pretty fun to.

ganeshie8 · Answer

you could also work it by eliminating z as you have been doing in previous problems, but lagrange multipliers much efficient...

astrophysics · Answer

Yup, but this one asked me to use Langrange, and I find this more efficient as you mentioned :).

astrophysics · Answer

Thanks again!

anonymous · Answer

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anonymous · Answer

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