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August 23, 2014

August 23, 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

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