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!

Help with Maximize

  1. May 20, 2006 #1

    tony873004

    User Avatar
    Science Advisor
    Gold Member

    Maximize P=xyz with x+y=30, y+z=30, and x,y, and z >= 0.
    [tex]
    \begin{array}{l}
    {
    \\
    y = 30 - x \\
    \\
    z = 30 - y\,\, \Rightarrow \,\,z = 30 - 30 - x = - x \\
    \end{array}
    [/tex]
    This is a problem, because if z is negative x according to the question, they must both be 0 or positive. This isn't a problem if x = 0, and that's what I get as 1 of two solutions by differentiating P when written in terms of x, and setting it to 0.
    [tex]
    \begin{array}{l}
    P = x(30 - x)( - x) = \left( { - x} \right)^2 (30 - x) = - 30x^2 + x^3 \\
    P = x^3 - 30x^2 \\
    \\
    P' = 3x^2 - 60x \\
    P' = x(3x - 60) \\
    \end{array}
    [/tex]
    [tex]
    x = 0
    [/tex]
    and
    [tex]
    3x - 60 = 0\,\, \Rightarrow \,\,3x = 60\,\, \Rightarrow \,\,x = \frac{{60}}{3} = 20
    [/tex]
    The z=-x isn't a problem in the x=0 solution, but it is a problem in the x=20 solution. This gives me x=20, y=10, z=-20 P=xyz=-4000.

    The back of the book gives x=20, y=10, z=20 P=4000.

    If z >= 0 and I get -20 for z, I can't just switch it to positive, can I? Don't I have to discard that solution?
     
  2. jcsd
  3. May 20, 2006 #2

    nrqed

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Watch out!!! 30-y is NOT 30-30-x!!
    (you will go :cry: when you will see what I mean)

    ;-)

    Pat
     
  4. May 20, 2006 #3

    tony873004

    User Avatar
    Science Advisor
    Gold Member

    :cry:

    30-(30-x)
    30-30+x

    :approve:
     
  5. May 20, 2006 #4

    nrqed

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    :biggrin: Yes...so z=x (which was clear from x+y = 30 and z+y = 30, wasn't it? :shy: )
     
  6. May 20, 2006 #5

    tony873004

    User Avatar
    Science Advisor
    Gold Member

    yes it was, thanks!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Help with Maximize
  1. Profit maximization help (Replies: 10)

Loading...