# Thread: Find the max value of function on line of intersection of two planes

1. ## 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.

2. Originally Posted by acropolen
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 ......