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Optimization problem

Here is the word problem:
A mass of clay of volume 432in^3 is formed into two cubes. What is the minimum possible total surface area of the two cubes? What is the maximum?

I have determined the following:
Surface Area (SA) = 6a^2
Volume of a cube (V) = a^3

I am not sure how to setup the formula to determine the asked for values to get to the derivative part of the problem. Any help would be greatly appreciated.

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Solution Preview

Hi, here is the solution...

When you form a clay with two cubes, definitely the shape of clay will be rectangular.

Volume of clay is given by 432 in^3

l*w*h = ...

Solution Summary

This solution is comprised of a detailed explanation to answer what is the minimum possible total surface area of the two cubes.

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