Given a region with 15 demand nodes, 4 bus lines, and 6 candidate bus stop locations as shown in Figure 1(a). The bus travel demand at each node is shown in Figure 1(b). Assume the travel distance between two adjacent zones is 5 minutes and travel can only take place in horizontal and vertical directions. A demand node is covered by a bus stop if it can be reached by the stop in 10min. a. The objective is now to maximize the covered travel demand with three bus stops to be located at this region. Write out the whole mathematical formulation for this problem. (8) b. Solve the above mathematical model to obtain: where are the optimal bus stop locations, and how much travel demand can these bus stops cover? (5') c. Given that the construction costs of building bus stops at the six candidate sites are respectively 5,10 , 15,10,20,15. Now the new objective is to cover the travel demands at all the demand nodes with the least construction costs. In this case, where should the bus stops be located? Write out the whole mathematical formulation for this problem. (7) (a) Bus stop locations (b) Bus demand