1. You are tasked with creating a rectangular box using 12 m! of (insert some random material here) because why wouldn’t

[answerhappygod]

1. You are tasked with creating a rectangular box using 12 m! of
(insert some random
material here) because why wouldn’t you be? To make this box
especially useful, let’s
design it so that it does not have a lid. Use a Lagrange multiplier
to find the maximum
volume of the box. To help get you started, let the volume of your
box be represented by
the function 𝑓(𝑥, 𝑦, 𝑧) = 𝑥𝑦𝑧 and subject to the constraint
𝑔(𝑥, 𝑦, 𝑧) = 𝑥𝑦 + 2𝑦𝑧 + 2𝑥𝑧 − 12. Be sure to include evidence that
your solution
represents a maximum.