Please show all work Thank you The 3E Global Delivery Compan

Please show all work. Thank you

The 3E Global Delivery Company provides different package delivery service. 3E is well known for its yellow trucks which are used to deliver local orders directly from the assigned starting location to the destination location. When the fuel price was low, the drivers of the trucks were free to take any routes of their choice as they made the delivery rounds. However, recently the fuel price is much higher than before. 3E\'s management would like to improve the efficiency of the delivery operation by determining the shortest delivery routes from the assigned starting location to the destination location. For example, the following networks shows the roads that may be taken from the assigned starting location a to the destination location j. Determine the shortest route for a truck that must make deliveries.

Solution

To find the shortest route[minimal spanning tree], we use Kruskal\'s algorithm.

Procedure: Firstl et us find the minimal edges in increasing order.

Then draw those edges one by one with all the vertices upto not making a circuit.

minimal edges weight

(d,c) 2

(b,c) 3

(h,g) 3

(f,i) 3

(a,b) 4

(f,g) 4

(g,k) 4

(a,d) 5

(d,f) 5

(b,h) 5

(h,k) 5

(k,j) 5

(a,d) 5

(d,f) 5

(a,c) 6

(c,g) 6

(d,g) 7

(i,j) 7

(a,e) 8

(c,h) 8

(f,j) 8

(g,j) 9

(e,i) 10

using Kruskal\'s algorithm, we get the following shortest route[minimal spanning tree]

                              e                                                     i

              8                 d                   5              f      3

                                 2                                 4

    a                         3      c                            g                                          j

4                                                          3                 4                    5

                    b                                   h                                  k