Step 1 :The problem is asking for two numbers that add up to 72 and have the maximum product. This is a classic optimization problem that can be solved using calculus or by recognizing that the maximum product of two numbers that add up to a given sum is achieved when the two numbers are equal.
Step 2 :In this case, since the sum of the two numbers is 72, the two numbers that give the maximum product are both 36. The maximum product is then \(36*36=1296\).
Step 3 :Final Answer: The values of \(x\) and \(y\) that have the maximum product are \(x= \boxed{36}\) and \(y= \boxed{36}\). The maximum product of \(x\) and \(y\) is \(Q= \boxed{1296}\).