EDISON is a California based electric vehicle (EV) manufacturer, who wants to establish its own fast charging infrastructure to promote the sales of its new electric cars. As an initial step, EDISON plans to establish p number of fast charging stations in California to cover long range trips of EVs which has a range of 200 miles with a fully charged battery. The company wants to locate its fast charging stations such that it can cover the highest possible percentage of the long range trips within California state, when the drivers start their trips at most with a half charged battery (that would have 100 miles of range). A recharging demand forecast team of EDISON has determined 51 potential cities between which a nonnegligible amount of EV traffic is expected in the near future. The attached CaliforniaData.xls file includes the following data: California highway road network data (Arc Set) Set of cities that are expected to be either the origin or the destination of an EV trip (O-D Node Set) Expected percentage of EV trips to occur between any given origin destination pair It is assumed that EV drivers would follow the shortest path to complete their trips. An EV trip is considered to be covered if there are enough recharging stations on the shortest path of the trip, such that the EV can complete its journey without running out of electric charge. All of the nodes in the California road network are candidate locations for the fast charging stations. Work on groups (as defined in the Blackboard) to complete the following tasks. Upload the written answers, code you write (including the comments that describe the code parts) and the screen outputs for your solutions. The coding part is optional and the groups who successfully complete it will get bonus points as indicated below. Please be informed that no partial credit will be given for the coding tasks. a) Formulate an IP model to find the optimal locations of fast charging stations that maximize the total percentage of the EV flow covered (50 points). Code your model in your favorite software and find the optimal fast charging station locations for p (3,6,9, 12, 15). How much of the total EV trips are covered in the optimal solution at each case? Comment on the insights you derive from these results (1 bonus credit). b) Now assume that the cost of building a fast charging station depends on its location. The city centers will have a cost of $300K, if the population is higher than 100.000 and $200K otherwise. Stations that are built on other nodes (which are not city centers) would just cost $100K. Describe how you would modify your model in part a to handle this new assumptions(30 points). Solve the problem if EDISON has a budget of B (0.5, 1,2,4} million dollars to set up fast charging stations. Comment on how does your solution in part a changes (0.5 extra credit). c) EDISON wants to find out at least how many recharging stations needed to cover all EV trips(20 points). Formulate an MIP model for this variant of the problem and solve it with your favorite solver. Comment on the differences of the solution you get in parts a and c (0.5 extra credit).