Postal Restrictions Some postal restrictions say that in order for a box to be shipped, it...

Postal Restrictions Some postal restrictions say that in order for a box to be shipped, its length (longest side) plus its girth (distance around the box in the other two dimensions) must be equal to no more than 108 inches.

If the box with length plus girth equal to 108 inches has a square cross section that is x inches on each side, then the volume of the box is given by V = x2(108 − 4x) cubic inches.

a. Find V(12) and V(18).

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b. What restrictions must be placed on x to satisfy the conditions of this model?

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c. Create a table of function values to investigate the value of x that maximizes the volume. What are the dimensions of the box that has the maximum volume?