PROBLEM 6: Consider the following example to motivate this problem... Summit, Inc. is in the (never-ending) process of expanding its empire. During the next year, they are planning to construct new stores that will serve 10 towns. The distances between the towns are given below. Towns 9 10 8 58 33 12 3 40 23 0 6 2 4 30 22 7 50 20 45 19 40 36 0 80 20 1 0 20 40 35 17 24 50 58 33 12 2 20 0 23 68 40 30 20 19 70 40 4 5 35 17 68 40 36 70 70 0 23 24 70 40 13 1040 20 70 21 40 13 50 40 80 10 40 70 80 70 22 45 30 21 80 80 50 23 0 12 14 50 50 12 14 0 26 40 20 3050 20 40 0 20 50 22 0 L 22 The population of each town (in thousands) is as follows: Town - Population 1 10 2 15 3 28 4 30 5 40 6 30 7 20 8 15 9 60 10 | 12 They are deciding in which towns it should locate its stores. Part A: The set covering problem seeks to find the minimum number of stores needed to cover all 10 towns. We say that a store can cover a town if it is located 25 or fewer miles away from that town. Write out the general formulation for a set covering model. Your formulation should be valid for ANY set covering model, not just for this example. Part B: Convert the above dataset into a set-covering dataset. PROBLEM 6: Consider the following example to motivate this problem... Summit, Inc. is in the (never-ending) process of expanding its empire. During the next year, they are planning to construct new stores that will serve 10 towns. The distances between the towns are given below. Towns 9 10 8 58 33 12 3 40 23 0 6 2 4 30 22 7 50 20 45 19 40 36 0 80 20 1 0 20 40 35 17 24 50 58 33 12 2 20 0 23 68 40 30 20 19 70 40 4 5 35 17 68 40 36 70 70 0 23 24 70 40 13 1040 20 70 21 40 13 50 40 80 10 40 70 80 70 22 45 30 21 80 80 50 23 0 12 14 50 50 12 14 0 26 40 20 3050 20 40 0 20 50 22 0 L 22 The population of each town (in thousands) is as follows: Town - Population 1 10 2 15 3 28 4 30 5 40 6 30 7 20 8 15 9 60 10 | 12 They are deciding in which towns it should locate its stores. Part A: The set covering problem seeks to find the minimum number of stores needed to cover all 10 towns. We say that a store can cover a town if it is located 25 or fewer miles away from that town. Write out the general formulation for a set covering model. Your formulation should be valid for ANY set covering model, not just for this example. Part B: Convert the above dataset into a set-covering dataset