Calculus

Minimize S=x+2y with xy=2 and both x and y > 0

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  1. Minimize S=x+2y with xy=2 and both x and y > 0

    Put F(x,y) = xy

    Then we have:

    dS/dx = lambda dF/dx (1)

    dS/dy = lambda dF/dy (2)

    Eq. (1) gives:

    lambda y = 1 (3)

    Eq. (2) gives:

    lambda x = 2 (4)

    If you divide (4) by (3 you get:

    x/y = 2 (5)

    We also know that

    xy=2 (6)

    If you multiply (5) by (6) you get x^2 = 4 which yields x = 2 because we knbow that x has to be positive. And this implies that y = 1

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