v = πr^2 h = 250
so, h = 250/(πr^2)
now, the cost is
c = .04(2πrh) + .05(2πr^2)
c = .02πr(250/πr^2) + 0.1πr^2
c = 5/r + 1/10 πr^2
To find minimum cost, find where dc/dr = 0
That is when r ≈ 2
Now finish it off ...
A cylinder shaped can needs to be constructed to hold 250 cubic centimeters of soup. The material for the sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.05cents per square centimeter. Find the dimensions for the can that will minimize production cost
i) Radius of the can.
ii) Height of the can.
iii) Minimum cost
Complete solution pls
2 answers
Can you solve i-iii for me? I dont know how to solve it
1 answer