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Simple Question
Question:
A rectangle box without a lid is to be made from 12 square metres of cardboard.
Find the maximum volume.
Please try it out before looking at the answer :)
Answer 1:
You can use trial and error.
Answer 2:
Let x, y and z be the length width and height of box. We want to maximize V(x,y,z) = xyz subject to the constraint g(x,y,z) = 2xz + 2yz + xy = 12
Find the answer by using the Method of Lagrange Multiplier :)
Final Answer:
The answer is 4 cube metres.
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Is Lagrange Multiplier like optimization?
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yes! but there are cases in which lagrange multipliers fail :(
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I assume this would be like the optimization stated above, where you want to optimize the volume.
V = xyz
A = 2xy + 2xz + 1yz (minus top)
And I actually forget how to do the rest from here. God damnit, I had to know this for calc 1...
dV/dx = yz
A = 2xy + 2xz + dV/dx
I forget what to do. Ah well :(