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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.

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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