Of all numbers that add to 54 , find the pair that has the maximum product. That is, maximize the objective function $Q=x y$ subject to the constraint $x+y=54$.
The values of $x$ and $y$ that have the maximum product are $x=$ and $y=$ (Type integers or simplified fractions.)

Step 1 ：The problem is asking to find two numbers that add up to 54 and have the maximum product. This is a classic optimization problem that can be solved using calculus or by completing the square. However, since we are dealing with integers, we can also solve it by brute force, i.e., by checking all possible pairs of numbers that add up to 54 and finding the one with the maximum product.

Step 2 ：The maximum product is achieved when both numbers are equal, i.e., when \(x = y = 27\). This makes sense because for a fixed sum, the product of two numbers is maximized when the numbers are equal (this is a property of the arithmetic-geometric mean inequality).

Step 3 ：Final Answer: The values of \(x\) and \(y\) that have the maximum product are \(\boxed{x=27}\) and \(\boxed{y=27}\).