Question

The volume of a crate with length of x feet, width of 8 - x feet, and a height of x - 3 feet is given by V(x)=x(8−x)(x−3) find the maximum volume of the crate and the dimensions for this volume

Answer 1

First, we need to find the maximum volume. In order to do this, we will first look at the dimensions of x and 8-x in the equation for volume. We can see that as x increases, so does 8-x. This means that there is a positive correlation between them. This also tells us that as x continues to increase, there will be a point where 8-x will equal 0. The maximum volume will occur when 8-x equals 0.

Therefore, the dimensions for the maximum volume are x=8 and x=-3.

Now we can solve for the actual maximum volume:

V max =(8)(8)-(3)(8)=64.

The maximum volume is 64 cubic feet and the dimensions for this volume are 8x=-3