4. Maximize $K=2 x-9 y$ given the following constraints: \[ \begin{array}{l} y \geq-x+6 \\ y \leq x+4 \\ y \leq 7 \\ x \leq 5 \end{array} \] The maximum is:

Step 1 ：Find the intersection points of the given constraints:

Step 2 ：\(\begin{cases} y = -x + 6 \\ y = x + 4 \\ y = 7 \\ x = 5 \end{cases}\)

Step 3 ：Intersection points: \(\{ (1, 5), (-1, 7), (5, 1), (3, 7), (5, 9), (5, 7) \}\)

Step 4 ：Evaluate the function K at each intersection point:

Step 5 ：\(K(1, 5) = 2(1) - 9(5) = -43\)

Step 6 ：\(K(-1, 7) = 2(-1) - 9(7) = -65\)

Step 7 ：\(K(5, 1) = 2(5) - 9(1) = 1\)

Step 8 ：\(K(3, 7) = 2(3) - 9(7) = -57\)

Step 9 ：\(K(5, 9) = 2(5) - 9(9) = -71\)

Step 10 ：\(K(5, 7) = 2(5) - 9(7) = -53\)

Step 11 ：Find the maximum value of K:

Step 12 ：\(\boxed{1}\)