Wednesday

October 1, 2014

October 1, 2014

Posted by **zeina** on Tuesday, December 28, 2010 at 10:21am.

The objective of this problem is to find the radius and the height of this cylinder such that its cost is minimized.Denote the radius of this can by r and its height by h. Let k be the cost,expressed in cents,of 1 cm square of the side of this can.

1)Express the cost of the side and that two bases in terms of r, h and k.

2)Express the total cost of manufacturing this can in terms of r only.

3)Find r that minimizes the cost.

4)Deduce the corresponding h.

- calculus -
**bobpursley**, Tuesday, December 28, 2010 at 11:20amLet r be the radius, h the height.

Cost=2K(2PIr^2)+ k*h*PI*(2r)

I will be happy to critique your work on this. A most excellent problem.

- calculus -
**Reiny**, Tuesday, December 28, 2010 at 11:21amwe know volume = πr^2h = 100

h = 100/(πr^2)

k = 2(2πr^2) + 1(2πrh)

= 4πr^2 = 2πr(100/(πr^2))

= = 4πr^2 + 200/r

dk/dr = 8πr - 200/r^2 = 0 for a max/min of k

8πr = 200/r^2

r^3 = 200/(8π)

take it from here

**Answer this Question**

**Related Questions**

calculus - A cylindrical container is to hold 20π cm^3. The top and bottom ...

calculus - a company is designing shipping crated and wants the volume of each ...

Math (algebra) - Could you help me with this math question: A can in the shape ...

Calculus - A company is designing shipping crates and wants the volume of each ...

Math - A cylinder shaped can needs to be constructed to hold 400 cubic ...

pre-calculus - A company plans to manufacture a container having the shape of a ...

calculus - a closed box with square base is to have a V= 2000in^3. The material ...

Calculus - A rectangular box with square base (which is NOT necessarily a cube) ...

Calculus - A cylindrical drum is made to hold exactly 1m^3 in its interior. ...

Calculus - An open top box with a square base is to be made so that it holds 3 ...