Question

The following picture gives highway distances in kilometres between a set of cities.

(a) Make a model in LINGO or the Excel Solver to determine the shortest path between cities 2 and 6 .
(b) Give the solution from LINGO or the Excel Solver, and state this path and its length in words.

Answer 1

To determine the shortest path between cities 2 and 6, we can use the concept of graph theory and a mathematical optimization tool like LINGO or Excel Solver. The solution will provide us with the shortest path and its length in kilometers.

Step-by-step explanation:

Solution for Part (a):

To determine the shortest path between cities 2 and 6, we can use the concept of graph theory and a mathematical optimization tool like LINGO or Excel Solver. The distances between cities can be represented as a weighted graph, where each city is a node, and the distances are the weights of the edges connecting the cities. We can then use the shortest path algorithm to find the shortest path between city 2 and city 6.

Solution for Part (b):

The solution from LINGO or Excel Solver will provide us with the shortest path and its length in kilometers. The shortest path between city 2 and city 6 is the route that minimizes the total distance traveled. The length of this path will depend on the specific distances between the cities provided in the given picture. Once we have the solution, we can state the path and its length in words.