The FAA has granted a license to a new airline, Omniair, and awarded it several routes between Los Angeles and Chicago. The flights per day for each route are shown in the following network: (a) Considering the capacities of both sides of each branch, determine the maximum number of flights the airline can schedule per day from Chicago to Los Angeles, and indicate the number of flights along each route by solving the problem manually – there is NO direct flight from Chicago to Los Angeles (show the work). (b) Formulate an integer programming model for this problem considering the directions of the branches as follows. (c) Find the maximum number of flights and the number of flights along each branch based on the formulation in (b) by using the computer. (d) Compare the results of (a) and (c). (e) Based on (c), what is the new maximal flow from Los Angeles to Chicago if the airport at Salt Lake City is closed?