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.