SRL Archive - Mathematics

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.

Is Lagrange Multiplier like optimization?

yes! but there are cases in which lagrange multipliers fail :(

4 m(power of 3-cubed)

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 :(