Question

A manufacturer needs to produce a cylindrical can with a volume (capacity) of 1000cm cubed. The top and the bottom of the container are made of material that costs $0.05 per square cm, while the side of the container is made of material costing $0.03 per square centimeter. Find the dimensions of the container that will minimize the company's cost of producing this container. What is the minimum cost?

Answer 1

minimum area

Answer 2

the problem is asking me to use optimization to find the minimum surface are and then determine how much it would cost to make it

Answer 3

let the radius of the cylinder be r,
let the height of the cylinger be h

πr^2h = 1000
h = 1000/(πr^2)

Cost = .05(2πr^2) + .03(2πrh)
= .1πr^2 + .06πr(1000/(πr^2)
= .1 πr^2 + 60/r
d(Cost)/dr = .2πr - 60/r^2
= 0 for a min cost

.2πr = 60/r^2
r^3 = 60/(.2π) = 300/π

carry on, find r, then sub into the simplified expression for Cost above

Answer 4

How do I apply using derivative