Math CentralQuandaries & Queries


Subject: precalculus - optimization
Name: ashley
Who are you: Student

A cylindrical container costs $2.00 per square foot for the sides and $3.00 a square foot for the top and bottom. The container must hold 100 cubic feet of material. What are the dimensions of the most economical container.

Hello Ashley.

The dimensions of a cylinder are the height, h, and the radius r. So the cost of the cylinder is

C(h,r) = 2(π r2)3+(2 π r h)2 = 6 π r2 + 4 π r h

The volume of a cylinder is V = π r2 h, so if V=100, then

100 = π r2h
h = 100/(π r2)

If we substitute this expression for h into the cost equation, then:

C(r) = 6 π r2 + 4 π r(100/(π r2))
C(r) = 6 π r2 + 400/r

Now you have a single equation with two variables. Can you do the final step and find the value of r that gives the smallest C(r)?

Hope this helps,
Stephen La Rocque.

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS