SOLUTION: a manufacturer wants to design a box having a base where the length is twice the width. the surface area must be exactly 300 square inches. what dimensions will produce a maximum v

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Question 1082325: a manufacturer wants to design a box having a base where the length is twice the width. the surface area must be exactly 300 square inches. what dimensions will produce a maximum volume?
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
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.
.
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So you know that,





The volume of the box is,



You can maximize by taking the derivative and setting it equal to zero,


So,




So then,

and
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

The other tutor forgot to put a top on the box.
The box when flattened out looks like this, drawn
to scale:



He did it correctly for a box without a top.
Follow his procedure but add the surface area
of the top of the box.

Answer for the box with a top, X = 5 in., 2X = 10 in., Z = 10 in.

It turned out that 2X and Z both were equal to 10, but
of course, you can't use that fact when solving.

Edwin
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