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Some math help please

  1. Oct 26, 2004 #1
    Some math help please (Updated)

    Find two numbers whose difference is 30 and whose product is a minimum. :confused:
     
    Last edited: Oct 26, 2004
  2. jcsd
  3. Oct 26, 2004 #2

    James R

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    Let's say the numbers are x and y.

    Then

    x - y = 30

    and we want the minimum value of P = xy

    There are lots of ways you could do this (e.g. Lagrange multipliers,...) but the simplest way is substitution:

    y = x - 30

    so

    P = x(x - 30) = x<sup>2</sup> - 30x

    To find the minimum value of P, differentiate:

    dP/dx = 2x - 30 = 0

    Therefore x = 15 and y = -15
     
  4. Oct 26, 2004 #3
    Thank you very much James.
     
  5. Oct 26, 2004 #4
    ok ran into some trouble on a similiar problem.

    Find two non-negative numbers whose sum is 60 and whose product is a max.

    I did the following

    x-y = 60
    xy = m
    y = x - 60
    m = x(x-60)
    m = x^2 - 60x
    m' = 2x - 60
    x = 30 , y = -30

    but y cant be negative...so? :confused:
     
  6. Oct 26, 2004 #5

    arildno

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    Dearly Missed

    But:
    You should have
    x+y=60 xy(max.)
    Not x-y!!
     
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