Given: $4 \le x \le 8$ and $2 \le y \le 7$

To find: Ratio = (maximum value of $(x + y)$) / (minimum value of $(x - y)$)

Step 1: Maximum of $(x + y)$ Occurs when both $x$ and $y$ take their maximum values: $x = 8$, $y = 7 \rightarrow x + y = 15$

Step 2: Minimum of $(x - y)$ Occurs when $x$ is minimum and $y$ is maximum: $x = 4$, $y = 7 \rightarrow x - y = -3$

Step 3: Ratio = $\frac{(x + y)_{max}}{(x - y)_{min}}$ = $\frac{15}{(-3)} = -5$

Since $-5$ is not among the given options, the correct answer is None of the above (Option D).