Problem 4: Bill has just completed his exams for the academic year and wants to celebrate by seeing every movie showing in theaters in his town and in six other neighboring cities. If he travels to another town, he will stay there until he has seen all the movies he wants. The following table provides the information about the movie offerings and the round-trip distance to the neighboring town: Theater location Movie offerings Round-trip miles Cost per show ($) In-town 1.3 0 7.95 City A 1,6,8 25 5.50 City B 2,5,7 30 5.00 City C 1,8,9 28 7.00 City D 2,4,7 40 4.95 City E 1,3,5,10 35 5.25 City F 4,5,6,9 32 6.75 The cost of driving is 75 cents per mile. Bill wishes to determine the towns he needs to visit to see all the movies while minimizing his total cost. a- Formulate the above problem as an ILP. b- Assume now that if Bill decides to visit city B, then he must visit city C too. Adjust the formulation in part a to account for this new requirement.