Results 1 to 5 of 5

Math Help - optimazation problems

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    3

    Exclamation optimazation problems

    A box with a square base and open top must have a volume of 13500cm^3.find the dimension of the box that minize the amount of material used.

    2. find the point on the line 6x + y = 9 that is closest to the point (-5,2)
    Last edited by mathsleaner; November 23rd 2008 at 05:20 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Nov 2008
    Posts
    5
    Quote Originally Posted by mathsleaner View Post
    A box with a square base and open top must have a volume of 13500cm^3.find the dimension of the box that minize the amount of material used.
    Let the sides of square base be x and height be h.

    volume = x^2h

    x^2h=13500

    h = \frac{13500}{x^2}

    Now, surface area, A = x^2+4xh

    A = x^2+4x\left(\frac{13500}{x^2}\right)

    A = x^2+\frac{54000}{x}

    now, minimize this area, can you take it from here?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    3
    thanks for the help but how do i minimize, that is the problem i have.how do i minimize the area.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2008
    Posts
    5
    Quote Originally Posted by mathsleaner View Post

    2. find the point on the line 6x + y = 9 that is closest to the point (-5,2)
    6x + y = 9 ...........................(1)

    Let the point (x, y) be on the line(1), which is closest to point (-5, 2)

    so, A line drawn from (-5, 2) to (x, y) is perpendicular to given line.

    so, slope of this line = 1/6

    eqn of this line (green dotted line in diagram)

    y - 2 = \frac{1}{6}(x+5)

    -x + 6y = 17..............(2)

    now, solving these two eqns, (1) and (2)

    we get (x, y) = (1, 3)
    Attached Thumbnails Attached Thumbnails optimazation problems-graph22.jpg  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2008
    Posts
    5
    Quote Originally Posted by mathsleaner View Post
    thanks for the help but how do i minimize, that is the problem i have.how do i minimize the area.
    Let me know which grade are you in? do you know calculus to minimize ???
    If not, then make a table of values of x and A
    calculate different values of A by taking different x values, by putting in above expression

    A = x^2+\frac{54000}{x}

    make a table of x and A, taking x = 25 to 32

    the minimum A will be when x = 30.

    so, h = \frac{13500}{x^2}=\frac{13500}{30^2}=15

    so, dimensions of box are 30 cm, 30 cm and 15 cm

    did you get it now???
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Another optimazation problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 9th 2011, 12:46 AM
  2. [SOLVED] Optimazation Problems
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 16th 2010, 09:18 PM
  3. optimazation problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 6th 2010, 04:35 AM
  4. Optimazation help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 30th 2009, 04:37 PM
  5. ugh, optimazation...
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 11th 2008, 07:28 PM

Search Tags


/mathhelpforum @mathhelpforum