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Optimization/maximization with multivariable calculus

  1. Nov 26, 2007 #1
    1. The problem statement, all variables and given/known data

    Maximize the Riemann Sum [tex]\Sigma[/tex] [tex]^{n}_{i=1}[/tex] x[tex]{i}[/tex]*y[tex]{i}[/tex] subject to constraints [tex]\Sigma[/tex] [tex]^{n}_{i=1}[/tex] x[tex]^{2}_{i}[/tex]=1 and [tex]\Sigma[/tex] [tex]^{n}_{i=1}[/tex] y[tex]^{2}_{i}[/tex]=1
    2. Relevant equations
    My teacher doesn't speak English very well. I'm in Calculus 3 and the average on his exams are around 40%. I'm a good Engineering student and need help. In class, we did an optimization problem where you can maximize the volume of say a box since you know length, width, height. We never went over this and I'm wondering how to do this. Despite him teaching us derivatives in that section, should I approach by doing integration and find the bounded region of x^2 and y^2 individually? Limits were never taught that much in high school so I really would appreciate your help.


    3. The attempt at a solution
    Maybe try the partial derivatives of the last two equations with respect to x and y, then set them to zero to find critical points? That's the only way I knew how to find local max and absolute max. Please help if you can. Thanks guys.
     
  2. jcsd
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