okay. one more time
πr^2h = 200
h = 200/(πr^2)
The area is thus
2πrh + 2πr^2
That makes the cost c
c = .02*2πr(200/πr^2) + .05*2πr^2
c = 4/r + 0.1πr^2
So to find minimum c, set dc/dr = 0
That occurs when r = ∛(20/π) = 1.853
Now finish it off
A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides
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 0.05 cents per square centimeter. Find the dimensions for the can that will minimize production cost.
1 answer
2 answers