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Got a question with substitution?

  1. Apr 19, 2005 #1
    Using the Substitution method, find the maximum value of

    4x-2xy+3y subject to the constraint 4x-y=2

    I can do the 1st part:


    substitute this into the original equation:

    Hope that right so far! but dont know where to go from there? any one could help plz?

    thanks ;)
  2. jcsd
  3. Apr 19, 2005 #2
    then you differentiate wrt x and equal to zero to find max/min
  4. Apr 19, 2005 #3
    what do u mean by wrt?
  5. Apr 19, 2005 #4


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    Staff Emeritus
    Science Advisor

    "wrt" : "with respect to"
    CartoonKid was assuming this was a calculus problem. The standard method for solving "maximum- minimum" problems in calculus is to differentiate and set the derivative equal to 0. But since you apparently weren't aware of that, I suspect this is not a calculus problem!

    If you multiply y= 4x-2x(4x-2)+3(4x-2) out, you get a quadratic. If you are doing problems like this, I presume you know how to complete the square to find the vertex of the graph which, in this problem, gives you the maximum value.

    So: multiply this out, then complete the square.
  6. Apr 19, 2005 #5


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    Science Advisor
    Homework Helper

    This method is totally counterproductive...The method discovered by Lagrange is much more elegant...

  7. Apr 19, 2005 #6
    But one would need a rather intermediate mathematical background to use them...
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