dimensions

Question

An open box with a square base is to be constructed from 27 square inches of material.  What dimensions will produce a box with maximum volume? 

Answer 1

Let x = length of a side of the base

     y = height

 

Surface area = area of base + 4(area of a side)

 

                  = x² + 4xy = 27

 

So, y = (27 - x²)/4x

 

Volume = V = (area of base)(height)

 

              V = x²y

 

              V = x²(27-x²)/4x

 

              V = (-1/4)x³ + (27/4)x, x > 0

 

Now, take the derivative, set it equal to zero, and show that the x-value obtained yields a maximum.  

 

 

Answer 2

27 inches of material?  WHAT IS THIS MATERIAL--it seems to be just a length, being given as 27 inches?

 

Methinks that you have paraphrased this problem incorrectly.  If the material is 27 square inches and that is to be split amongst four sides plus a square base, that's something else.