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Homework Help: Quadratic equation solving with constraint.

  1. Oct 28, 2012 #1
    1. The problem statement, all variables and given/known data
    So I've worked this problem for awhile. Its a several page of math problem with optimization, legrangians, cramers rule, etc to get to this point. All I need to do now is by hand solve this equation for x and y with the constraint.

    2. Relevant equations

    -0.03x^2 + 40x - 0.02y^2 + 5y+ 55000 = 0
    Subject to the constraint: x+y=3000

    3. The attempt at a solution

    I could put up the pages of work I've done to get to this point, but it really doesn't have any relevant info to help get to this point. I have the answers which is x=1100 & y=1900. Just don't know how to do this last step I've got to.

    Thanks so much for the help!
    Last edited by a moderator: Oct 28, 2012
  2. jcsd
  3. Oct 28, 2012 #2


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    Homework Helper

    If your constraint is x+y=3000 then you just need to plug y = 3000-x into the quadratic.
    Last edited by a moderator: Oct 28, 2012
  4. Oct 28, 2012 #3


    Staff: Mentor

    Geometrically, the quadratic equation in x and y represents an ellipse, and the constraint represents a straight line, so you will either get no solutions, one solution, or two solutions.
  5. Oct 29, 2012 #4
    Thanks so much! This is exactly what was messing me up. Dono why I didn't think of that.

    Thanks again!
  6. Oct 29, 2012 #5


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    Homework Helper

    You're welcome :smile:
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