Results 1 to 3 of 3

Math Help - limiting cost and max problem!

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    16

    Exclamation limiting cost and max problem!

    A closed cylindrical canister of 8pi cubic feet is to be made. It must stand between two partitions 8 feet apart in a room with a 8 ft. ceiling. If the cost of the top and bottom is $1 per square foot and the cost of the lateral surface of the cylinder is $2 per square foot, find the dimensions of the least expensive canister.

    How would you draw a picture for this? And how would you solve this problem according to the min and max rates and such? Confused on where to start and how to get an answer?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,698
    Thanks
    454
    Quote Originally Posted by hotdogking View Post
    A closed cylindrical canister of 8pi cubic feet is to be made. It must stand between two partitions 8 feet apart in a room with a 8 ft. ceiling. If the cost of the top and bottom is $1 per square foot and the cost of the lateral surface of the cylinder is $2 per square foot, find the dimensions of the least expensive canister.

    How would you draw a picture for this? And how would you solve this problem according to the min and max rates and such? Confused on where to start and how to get an answer?
    It must stand between two partitions 8 feet apart in a room with a 8 ft. ceiling.

    h < 8 , r < 4<br />

    \pi r^2 h = 8\pi

    h = \frac{8}{r^2}<br />

    the cost of the top and bottom is $1 per square foot and the cost of the lateral surface of the cylinder is $2 per square foot

    C = (2\pi r^2)(1) + (2\pi r h)(2)

    sub in the expression for h in terms of r into the cost equation, find \frac{dC}{dr} and minimize ... don't forget to note the room constraints.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2009
    Posts
    16

    Exclamation

    when I sub in the equation should look like this right?
    (2pir^2)(1) + (2pir(8/r^2)

    so when i differentiate it would look like this
    4(pi)5 dc/dr + (what would be here)?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cost problem
    Posted in the Business Math Forum
    Replies: 1
    Last Post: July 13th 2010, 04:08 AM
  2. Process cost systems,total cost under the FIFO Method.
    Posted in the Business Math Forum
    Replies: 0
    Last Post: December 4th 2009, 11:13 PM
  3. Marginal Cost/Demand and Cost
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 4th 2009, 06:45 PM
  4. What are the Limiting Distribution and Limiting Probabilities
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: April 3rd 2009, 12:49 PM
  5. Series problem with limiting sum
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 8th 2007, 06:39 AM

Search Tags


/mathhelpforum @mathhelpforum