I answered the question my way and I have 0.0298 m for the optimal radius of the can... Now I know the book's answer is wrong because it says 21m*16m or some silly thing.
Here's the question:
A soup manufacturer wants to sell its soups in 500-ml cans. The metal for the top is $1.20/m^2 The metal for the sides costs $0.40/m^2. After the circles for the top and bottom are cut out of a rectangle, the remaining metal is scrapped. Find the dimensions of the can that will minimize material cost.
So I have a few equations I used:
to minimize cost:
C=2*pi*(r^2)*1.20 + 0.40*(2pi(r)h)