Of all numbers that add to 72 , find the pair that has the maximum product. That is, maximize the objective function $Q=x y$ subject to the constraint $x+y=72$.
The values of $x$ and $y$ that have the maximum product are $x=$ and $y=$ (Type integers or simplified fractions.)
The maximum product of $x$ and $y$ is $Q=$ (Type an integer or a simplified fraction.)

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 \(Q= \boxed{1296}\).