In a dystopic parallel time, radiation from the sun causes a global disaster on Earth and survivors on an overnight flight from Brussels, Belgium race from city to city trying to stay ahead of the sun's rays by remaining in the cover of night. Those who are objected to sunlight die within minutes, that is why almost all living organisms have perished except for those who are lucky such as the above-mentioned flight passengers. The pilot of the airplane received a radio message that there is a large bunker in Severobaykalsk, Russian Federation; and the closest airport to this city is Nizhneangarsk Airport, which is 26km northeast of Severobaykalsk. The bunker is said to have everything necessary to shelter about 10000 people for one year. After a ballot, the survivors on the plane have decided to reach to the bunker but this will not be an easy task as they must always be ahead of sunlight. Thus, they have to travel at night from Brussels to Severobaykalsk; but due to fuel capacity of the flight they have to take breaks in several airports to refill the fuel tank of the airplane. The flight crew has the information that the maximum duration that the airplane can fly is 12 hours. Furthermore, it takes approximately 1 hour to refill the fuel tank of the airplane in any airport. Keeping in mind that they have to use the time zone changes to travel at night (beware that if they travel during daylight they will all die immediately!) the pilot calculated that they need at least three stops between Brussels and Severobaykalsk. The pilot is also aware that in an applicable plan the time zones, fuel refill time, travel time from Nizhneangarsk Airport to the bunker in Severobaykalsk (if cars available at Nizhneangarsk Airport are used), and the necessity to travel during night have to be taken into account. To find a flight plan from Brussels and Severobaykalsk apply dynamic programming by assuming the following information. - The airplane is now at Brussels Airport and it is 21.30 in local time. The current date January 2nd,2022. - The plan must involve at least three stops for fuel refill between the origin to destination. - For each stop at least three alternative airports must be determined. - The sunrise and sunset times for the cities that the alternative airports are in can be found through the following website (or you are free to use other sources, but the timings must be real): https://www.timeanddate.com/sun/ - Beware that the times for each stop or airport must be considered as the local time using the corresponding time zone. - You must consider the real flight times between the airports by taking into realistic parameters such as the average airplane speed, flight distance between the airports, and etc. You are free to use any source for finding this information. - Since almost everybody on land has passed away due to this catastrophe, the airplane crew will not be trying to get any permission from the authorities to land at any airport or use any country's airspace (the authorities also have died, most probably). - You can add further realistic assumptions to simplify your solution. But these assumptions must not risk the lives of the airplane passengers. Considering the information and assumptions mentioned above, answer the following questions: 1) Determine the number of stops. Explain how you decided on this number. 2) For each stop determine at least five - at most seven alternative airports to land (real airports that are within flight range of the preceding stop). Explain how and why you determined these alternative airports. Furthermore, give details about all extra assumptions that you add (if you add any) 3) Define the states and stages for the above problem to be solved as a dynamic programming. 4) Represent all stages, states and connections between the stages and states on a network. The network must also include the travel distance between the airports (it can be in terms of time. Also, do not forget to include fuel refilling and any other necessary time). 5) Is the dynamic programming approach that can be used here probabilistic or deterministic? Explain. 6) Define all necessary functions to be evaluated together with all necessary notations. 7) For each stage, make the necessary calculations and come up with the optimal flight plan. Display the route and provide the travel duration. At what time will the survivors be in the bunker? *The calculations can be displayed on tables. The dynamic programming model you constructed to answer the questions has to be implemented on an appropriate software (MATLAB, Python, C++, and etc.) It is not sufficient to be successful from the project unless you use a software. You have to submit the code files in pdf format along with the project report. 8) Is it possible to find a solution with another approach apart from dynamic programming? Explain. You must write your answers to the above questions in the format that is explained in project template. Please embed appropriate explanations and comments for each of your calculation and the figure or table that you include in your report. The due date for submissions is December 20th, 2022, Tuesday at 22:00 o'clock. Please be aware that no late submissions are permitted. It is sufficient for only one member in each project team to submit your report and code file (in pdf format) on CATS. The submissions are available on CATS under assignments