Jim lives in Denver, Colorado, and likes to spend his annual vacation in Yellowstone National Park in Wyoming. Being a nature lover, Jim tries to drive a different scenic route each year. After consulting the appropriate maps, Jim has represented his preferred routes between Denver (D) and Yellowstone (Y) by the network in Figure 6.42. Nodes 1 through 14 represent intermediate cities. Although driving distance is not an issue, Jim’s stipulation is that selected routes between D and Y do not include any common cities. Determine (using AMPL or Solver) all the distinct routes available to Jim.

(Hint: Modify the maximal flow LP model to determine the maximum number of unique paths between D and Y.)