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!

PLEASE HELP maximizing area problem

  1. Jan 25, 2012 #1
    PLEASE HELP!! maximizing area problem

    1. The problem statement, all variables and given/known data
    1. The problem statement, all variables and given/known data
    A farmer wants to build a rectangular pen. He has a barn wall 40 feet long, some or all of which must be used for all or part of one side of the pen. In other words, with f feet of of fencing material, he can build a pen with a perimeter of up to f+40 feet, and remember he isn't required to use all 40 feet.
    What is the maximum possible area for the pen if:
    a. 60 feet of fencing material is available
    b.100 feet of fencing material is available
    c. 160 feet of fencing material is available


    2. Relevant equations
    a.
    P=> 2x+y=60 => y=60-2x
    A=> xy=60x-2x^2


    3. The attempt at a solution
    I worked through the problem and found
    a. For 60 ft of fencing material
    x=15, y=30 => A=450 sq ft

    I am not sure how to do b and c.
    This is my attempt, but I know it is wrong (slightly)
    b. For 100 ft of fencing material,
    P=> 2x+y=100 => y=100-2x
    A=> xy=100x-2x^2
    working through this, I end up with
    x=25, y=50 => A=1250 sq ft

    I know this is wrong because the barn wall is only 40 feet long, and y=50, but all of the 100 feet of fencing has been used up by 2x+y, so there will be 10 feet of fencing missing. How do I rework the problem? Please help i've been working on this for hours!! :(
     
  2. jcsd
  3. Jan 25, 2012 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Re: PLEASE HELP!! maximizing area problem

    The variable y is the one with the constraint on it. It has to lie somewhere in the interval [0, 40]. Write the area as a function of y and find where it attains its maximum on that interval.
     
  4. Jan 25, 2012 #3
    Re: PLEASE HELP!! maximizing area problem

    This is linear programming problem. With following equations for b

    [tex]x\geqslant 0\quad ; 0\leqslant y\leqslant 40[/tex]

    [tex]2x+2y \leqslant 140[/tex]

    Maximize the function [itex]A=xy[/itex]. Use LP theorem
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: PLEASE HELP maximizing area problem
  1. Maximize Area (Replies: 8)

Loading...