A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides

Question

of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be
thicker, and costs 0.06 cents per square centimeter. Find the dimensions for the can that will minimize
production cost.

Radius of the can:

Height of the can:

Minimum cost:

Answer 1

πr^2h = 200, so h = 200/πr^2

The cost is thus

c = .02*2πrh + .06*2πr^2
= .04πr(200/πr^2) + .12πr^2
= 8/r + .12πr^2

dc/dr = -8/r^2 + .24πr
dc/dr=0 when r ≈ 2.2

Now just crank out h and c