Problem 3 130 points]: A city has nine residential areas, connected by the road

Question

Problem 3 130 points]: A city has nine residential areas, connected by the road network shown below. Travel times between pairs of residential communities are shown on the arcs of the network. 1. [10 points] Set up a linear programming problem to identify shortest paths between eaclh pair of nodes, and solve the problem using Solver. The city decides to build public community centers to serve these residential areas. The city desires to build the least number of centers such that all residents can travel to the community center within 10 minutes. 2. [10 points] Set up an integer program that achieve they city's goal 3. [5 points] Solve the problem in Solver. 4. [5 points] What if the requirement is to have all residents live within 5 minutes to the community center? 12 15 4 4 4 10 12

Explanation / Answer

In order to find the linear equation for the shortest path , we should look at the dependent and undependent vectors.

Dependent vector - time taken to travel from a pont to other. (let's call it y)

Independent vectors - Distance between two points(x1), speed of travel (x2), no of stops in between (x3)

on the basis of the dependent and independent vectors we will get an equation

y = b0*x1 + b1*x2 + b3*x3

The eqatuion is the linear equation to find the time taken to travel from one point to other.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.