Assuming that the available time for the classroom is unlimited, we instead focus on the course completion time. We aim to schedule $n$ courses, where each course $i$ is characterized by its duration $p_i$ and weight $w_i$. In this schedule, the finish time of each course is the total duration of all courses scheduled before it, plus its duration. A schedule can be defined as a function $d(i)$, representing the order of course $i$ in the schedule. That is, if $d(i) < d(j)$, course $i$ is scheduled before course $j$. Therefore, the finish time of course $i$ is denoted as $f_i = \sum_{j \in \{1,\ldots,n\}:\, d(j) < d(i)} p_j$. This scheduling problem aims to minimize the total weighted finish time $\sum_{i \in \{1,\ldots,n\}} w_i f_i$. Suppose we have 15 courses with corresponding durations [6, 6, 9, 83, 34, 44, 164, 38, 82, 180, 19, 128, 394, 512, 15] and weights [2, 4, 4, 6, 7, 7, 7, 10, 10, 10, 11, 12, 13, 13, 15]. What is the value of the optimal schedule, that is, the minimum total weighted finish time?