Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 17

Solve Problem from Chapter to determine the shortest route for the "Weekend Rider" bus service from Tech to DC that will also result in at least 30 passengers.
Problem
The bus company in Draper operates a "Weekend Rider" bus service from the Tech campus to Washington, DC. The bus seats 55 passengers and selects the shortest route to DC that will also result in at least 30 passengers. The bus can travel through 11 different cities and towns depending on the number of passengers it expects to attract. The following network shows the different connecting pickup points and the distance between them in miles:

The bus service expects to pick up the following passengers at each possible stop: 20 at stop 1 (Tech), 4 at stop 2, 3 at stop 3, 5 at stop 4, 5 at stop 5, 7 at stop 6, 6 at stop 7, 4 at stop 8, 8 at stop 9, 6 at stop 10, 6 at stop 11, and 5 at stop 12. Determine the shortest route between Tech (at 1) to DC (at 13) that will result in at least 30 passengers. Compare this route to the shortest route without the required number of passengers, and indicate how many passengers the bus would have with this route.