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Math Help - Find the max value of function on line of intersection of two planes

  1. #1
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    Find the max value of function on line of intersection of two planes

    Hello, I am having a hard time figuring out how to start the following problem:

    Find the maximum value(s) of the function f(x,y,z) = xyz on the line of intersection of the planes x + y + z = 40 and x + y - z = 0. Explain your methods carefully, and give a geometric argument to support your claim that you have found a maximum (and not a minimum) value.

    I thank you for your assistance.
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  2. #2
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    Quote Originally Posted by acropolen View Post
    Hello, I am having a hard time figuring out how to start the following problem:

    Find the maximum value(s) of the function f(x,y,z) = xyz on the line of intersection of the planes x + y + z = 40 and x + y - z = 0. Explain your methods carefully, and give a geometric argument to support your claim that you have found a maximum (and not a minimum) value.

    I thank you for your assistance.
    The line of intersection of the two planes is z = 20. So on this line the value of the function is 20xy --> +oo ......
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