老师好，我刚上大学线性代数的课程， 老师布置了一个作业，我实在没思路，不知这个题是不是有问题，是不是线性代数能求解。所以能请教一下老师吗？我尝试了使用线性规划,也列出了目标函数，和约束条件，想通过python的scipy库求解，但是，总是报错。
问题，我先给您看一下
Suppose you are a timetable scheduler for a transport company. You are required to schedule 80 trains at a specific train station between 4:00 am to 11:59 pm (20 hours). You are given the passengers’ arrival time data for a typical day (PessengerArrivalTime.csv – this is simulated data).
Your goal is to minimize the average waiting time for all these passengers.

You are required to carry out the following tasks:

1. Solve the above using Linear Programming based on the above requirements and to obtain an optimal solution;

2. Given a set of additional constraints:
   i. the minimal interval for consecutive trains is 5 minutes and,
   ii. the maximal interval is 30 minutes,
   iii. also the first train must leave the station at exactly 4:00 am,
   How to formulate the new optimization task? Please then solve it and to obtain its optimal solution.

3. Additionally, try to solve it from a Probability perspective: Fit the passenger arrival patterns with a probability distribution (hint: a mixture model), construct a Non-Linear Programming task with/without the additional conditions in (2), and to obtain both optimal solutions.

PessengerArrivalTime.csv 是一个给了所有乘客到站的时间表的文件，给出的数据如，4:1600， 4:29:00， 4:34:00，…, …, 23:57:00等