One common problem in ridesharing systems is that of redistributing empty vehicles. The problem arises because the flows of vehicles are not symmetric. In particular, the flow of vehicles in one direction to one location may be more (or less than the flow from that location to all other sites. The locations that end up with an excess of empty vehicles are supply locations and those that have too few empty or available vehicles for rental are demand locations. The problem is to optimally relocate the excess empty vehicles from the supply locations to the demand locations. Think about a bicycle ridesharing system if you want a concrete example of this. In the early morning, there may be a high demand for bicycles in residential areas. People then ride these bicycles to work in a downtown area. They may elect to go out to dinner and then take a taxi or Uber home since it is too dark to ride a bicycle safely. This creates a surplus of bicycles in the downtown work area and a deficit of bicycles in the residential areas. These bicycles must be redistributed to the residential areas during the night so that they are available for rental the next day. Let us define the following notation: INPUTS set of supply locations K set of demand sites unit cost of moving one vhicle from supply je J to demand k eK number of vehicles that must be moved to site k e K number of vehicles available at location j e J for reditribution DECISION VARIABLES Xik number of vehicles to move from je J to ke K a) Using this notation, write down the objective function of minimizing the total cost of redistributing vehicles. b) Write down the constraint that says that the number of vehicles moved out of each supply location must be less than or equal to the number available at that location. c) Write down the constraint that says that each the number of vehicles moved to each demand location must be greater than or equal to the demand at that site.