Greetings! You have been given a summer internship in a trucking company where you will work as a truck driver. Your task is to deliver goods from one place to another across the country. But here's a catch, your truck has a limited fuel capacity, and you are told to minimize the number of stops at gas stations. You will have to deliver the goods at the destination somehow.

A few things to note:

Your truck has a fuel capacity limit of $150km.$

The total distance from source to destination is $400km.$

There are four gas stations on your way to the destination.

Station A is situated $200km$ away from the starting point.

Station B is situated $300km$ away from the starting point.

Station C is situated $250km$ away from the starting point.

Station D is situated $100km$ away from the starting point.

a$)$ Your task is to cover the total distance by minimizing the number of stops at fuel stations. Show the simulation in detail and finally state the solution.

b$)$ Do you think the solution $($a$)$ is optimal? If not, then suggest a better solution and the reason for it$.$