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Help solving for 3 equations and 3 unknowns

  1. Apr 5, 2014 #1
    1. The problem statement, all variables and given/known data
    Solve the following equation for [itex]P_{1}[/itex] and [itex]P_{2}[/itex]

    2. Relevant equations
    [itex]7.0+0.004P_{1}-\lambda(1-0.0004P_{1})=0[/itex]
    [itex]7.0+0.004P_{2}-\lambda=0[/itex]
    [itex]P_{1}+P_{2}-500-0.0002P_{1}^{2}=0[/itex]


    3. The attempt at a solution
    I am having some issues on ways to solve this problem. I guess the main point I am stuck on is how do I even approach it?

    I have three unknowns [itex]P_{1}, P_{2}, \lambda[/itex] and three equations, so I should be able to solve for [itex]P_{1}, P_{2} [/itex].

    The example shows that the solutions are:
    [itex]P_{1}=178.882 , P_{2}=327.496[/itex].

    Any suggestions or tips would be greatly appreciated
     
    Last edited: Apr 5, 2014
  2. jcsd
  3. Apr 5, 2014 #2
    My first suggestion would be to give some equations. You've given 3 expressions, which don't appear to equate to anything.
     
  4. Apr 5, 2014 #3
    Woops. Updated. All expressions equal 0
     
  5. Apr 5, 2014 #4
    That's better! :smile:

    How are you with algebraic manipulation?

    The first equation gives you [itex]P_1[/itex] in terms of [itex]\lambda[/itex], and the second gives [itex]P_2[/itex] in terms of [itex]\lambda[/itex].

    Plug them both into the third equation and you find the value of [itex]\lambda[/itex].

    Use this value of [itex]\lambda[/itex] to find the values of [itex]P_1[/itex] and [itex]P_2[/itex].

    Job done! :smile:
     
  6. Apr 5, 2014 #5
    Thanks for the help. This is becoming a very complicated solution :S Will just use Matlab to solve!
     
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