1. The problem asks why the maximum score occurs at the minimum value of $T$. 2. Typically, in optimization problems, the score or objective function depends on a variable $T$. 3. If the score decreases as $T$ increases, then the maximum score will be at the smallest possible $T$. 4. This can happen if the score function $S(T)$ is monotonically decreasing, meaning $\frac{dS}{dT} < 0$ for all $T$. 5. For example, if $S(T) = \frac{1}{T}$, then as $T$ gets smaller, $S(T)$ gets larger, so the maximum score is at the minimum $T$. 6. Another reason could be constraints or penalties that increase with $T$, reducing the score. 7. In summary, the maximum score occurs at minimum $T$ because the score function decreases as $T$ increases, making the smallest $T$ yield the highest score.