1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Quadratic Properties Question

  1. Apr 4, 2012 #1


    User Avatar

    1. The problem statement, all variables and given/known data
    Canada Post will deliver parcels only if they are less than a certain maximum size: the combined length and girth cannot exceed 297 cm (Girth is the total distance around the cross-section of the parcel). Canada Post delivers a crate with the smallest SA to your house. What is the SA of the crate in square meters?

    2. Relevant equations
    Girth of a rectangular prism=2(w+h) -> Web-search
    I'm still unclear on what a girth is, however. Maybe it is 2(l+w), the perimeter of the base.

    3. The attempt at a solution
    I set-up the equations:



    I'm unsure how to proceed. Any help is appreciated. Thanks!

    Last edited: Apr 4, 2012
  2. jcsd
  3. Apr 4, 2012 #2


    User Avatar
    Science Advisor

    The smallest? You say that Canada Post will not deliver packages above a certain size but they can be as small as you please. Are you asking for the smallest surface are of a package that meets the maximum sum of length and girth?

    Yes. assuming you are taking h as the longest side, "girth" is 2(l+ w) so the requirement is that [itex]h+ 2(l+w)\le 297[/itex].

    Hey, you switched h and l on me!

    Proceed in either of two ways:
    1) use l+ 2*(w+ h)= 297 (or h+ 2(w+ l)= 297) to eliminate one of the three variables leaving only two. Set the partial derivatives with respect to the two variables equal to 0 and solve the two equations.

    2) Use the "Lagrange Multiplier" method. Form the gradient of the "object function", 2(wh+ lw+ lh), the gradient of the constraint, l+ 2(w+h), and set one equal to a constant ([itex]\lambda[/itex] times the other.
  4. Apr 4, 2012 #3


    User Avatar

    I'm not sure how to eliminate one of the three variables?
    Last edited: Apr 5, 2012
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook