1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Optimization question. Please help!

  1. Mar 9, 2005 #1

    jzq

    User Avatar

    Minimizing Construction Costs: If an open box has a square base and a volume of 108 in.^3, and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.

    This is what I have so far:

    [tex]Volume: 4y^3-4xy^2+x^2y=1=108[/tex]

    [tex]x=-\sqrt{\frac{108}{y}}+2y[/tex]

    Now I'm not sure if these are right so, please feel free to correct me. I would much appreciate it!
     
  2. jcsd
  3. Mar 9, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Who's "x",who's "y" and what is the shape of the box...?The simplest would be the case of a rectangular parallelipiped.


    Daniel.
     
  4. Mar 9, 2005 #3
    Optimization problems like these deal with derivatives. I don't quite understand the question though. Is it saying you have an square box with an open top?
     
  5. Mar 9, 2005 #4

    jzq

    User Avatar

    I copied this question write out of the book. It's hard to interpret. I'm thinking it has a square base, however the height varies. Therefore I put x-2y as the width and length and y as the height. The box is made from a tin sheet, so I believe the corners are cutout and folded up to form a box. That is why the sides are x-2y and the height is y. This is how I got the volume formula.
     
  6. Mar 9, 2005 #5

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    I hope they meant an parallelipiped.So what's the volume function...?It should be:
    [tex] V=abc=108 [/tex],okay...?

    No make use of the fact that the base is a square,which means
    [tex] V=a^{2}c=108 [/tex]

    What's the area...?Remember,the area of the top must be taken out...


    Daniel.
     
  7. Mar 9, 2005 #6

    jzq

    User Avatar

    Sorry, I have no idea what you mean by parallelpiped. I wish I can draw a picture and upload it, but unfortunately the files are too large.
     
  8. Mar 9, 2005 #7

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Can't u zip (turn to archive .zip) it or put it a .gif or .jpeg ???

    Paralellipiped is a regular prism with all faces parallelograms...The natural generalization of a cube.

    Daniel.
     
  9. Mar 9, 2005 #8
    He's saying you have a square base with a long/shorter height that isn't equivalent to the length of width of the base.

    V for box like shape is abc. Since you have a * a * c(height), you can write this like Daniel did above: [itex]V = a^2c[/itex]

    This would give you the volume of the enitre box. But since we are picturing this figure to have the top removed, you need to subtract the area of the top to get an equation you can work with.

    So use this equation:

    [tex] V = a^2c - a^2[/tex]

    Does that make sense?


    Jameson
     
  10. Mar 9, 2005 #9

    jzq

    User Avatar

    Thanks alot everyone!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Optimization question. Please help!
Loading...