Math

Solve the optimization problem.

Minimize F = x^2 + y^2 with x + 2y = 15.

Thank You for the help!!

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asked by Jerry
  1. x = 15 - 2y
    x^2 = 225 - 60 y + 4 y^2

    F = 5 y^2 -60 y + 225
    dF/dy = 10 y - 60
    zero when y = 6 then x = 3

    is that min or max?
    d^2F/dy^2 = 10 so it is min

    F here = 9+36 = 45

    check ends
    if x = 0 y = 7.5 and F = 56 1/4
    if y = 0, x=15 and F = 225
    ok, done

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    posted by Damon
  2. Wow thank you so much!!!!

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    posted by Jerry

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