Results 1 to 3 of 3

Math Help - Minimization, finding dimensions

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    2

    Minimization, finding dimensions

    The cabinet that will enclose the Acrosonic model D loudspeaker system will be rectangular and will have an internal volume of 1.8 ft3. For aesthetic reasons, it has been decided that the height of the cabinet is to be 1.4 times its width. If the top, bottom, and sides of the cabinet are constructed of veneer costing 35 per square foot and the front (ignore the cutouts in the baffle) and rear are constructed of particle board costing 19 per square foot, what are the dimensions of the enclosure that can be constructed at a minimum cost?

    This is a minimization problem. Is this a minimization of area or volume? What I have so far.

    V=LWH. 1.8 = x^2(1.4x) my constraint? I’m assuming the bottom is a square so LW is both x and H is 1.4x.
    Cost = 2bottoms * .35 + 2side *.35 + 2side *.19 = .35(2x^2) + .35((2(x*1.4x)) +.19((2(x*1.4x))

    This problem is a little different than my previous minimization maximization problems. I can’t seem to combine them to find a derivative. Please help thank you!
    Last edited by mr fantastic; December 4th 2009 at 12:45 PM. Reason: Changed font so that a microscope is not needed to read the question.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2008
    Posts
    903
    Hi. I did this quick so check me ok:

    v=Lwh=1.8

    C_t=V+P

    V=\frac{35}{100}(t+b+2s)

    P=\frac{19}{100}(f+r)

    Then I get:

    C_t=\left\{\frac{35}{100}(Lw+Lw+2hw)+\frac{19}{100  }(2hL)\right\}

    but h=1.4 w and L=\frac{1.8}{1.4 w^2}

    when I put all that into the cost function as a function of w I get:

    C_t=\left\{\frac{35}{100}(2\frac{1.8}{1.4 w})+2(1.4 w^2)+\frac{19}{100}(2(\frac{1.8}{w}))\right\}

    Next thing I would do is outright plot it and see if it has a minimum. If the plot doesn't, then I made a mistake and no need to go further. I'll leave that for you to check. If it does, then find the extrema to find the minimum cost.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2009
    Posts
    2
    Thank you Shawsend, I will re-try the problem with your help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding dimensions of a can
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 7th 2011, 04:07 AM
  2. Finding Dimensions And Bases
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 1st 2010, 12:17 AM
  3. Finding Dimensions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 18th 2010, 03:13 PM
  4. Root finding in three dimensions
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: September 20th 2009, 09:06 AM
  5. Finding dimensions
    Posted in the Calculus Forum
    Replies: 8
    Last Post: March 23rd 2008, 06:01 PM

Search Tags


/mathhelpforum @mathhelpforum