Page 63 - Calc for the Clueless

Total cost T = 4C(2x + 2y) + 2Cy = 8Cx + 10Cy But A = xy = 800. So y still equals 800/x. Substitute into T.

Example 3—

An open box with a square bottom is to be cut from a piece of cardboard 10 feet by 10 feet by cutting out the
corners and folding the sides up. Find the dimensions that will result in the largest volume.

The most difficult part of this problem is the picture, which is given above in three steps. The volume of a box
is length times width times height.

We reject 5 since it will give a volume of 0, a minimum.

indicating a maximum.

The length and width are each 10 - 2x = 10 - 2(5/3) = 20/3. The box we are looking for is 20/3 by 20/3 by 5/3
feet.

Let's do one more box problem.

Example 4—

A box has a square base and no top.

A. Find the minimum surface area needed if the volume is 4 cubic feet. Let's also do the related problem—

B. Find the maximum volume if the surface area is 12 square feet.