3. For the graph below: 10 10 10 13 (a) Find a minimum spanning tree and write out the ares being added at each step using Prims Algorithm (b) Find a minimum spanning tree and write out the arcs being added at each step using Kruskal's Algorithm. (c) Show that 2 of your tree arcs are optimal using the cut optimality condition and that not selecting 2 of your non-tree ares was optimal using the path optimality condition. (d) Write the optimization model for the MST using the complete problem data. You do not need to write all of the no-cycle constraints- you should write at least 3 of them that have a subset size of 3 or greater. (e) Note: you may find reading the textbook section about Minimum Spanning Trees useful- this is found in chapter 10 in both textbooks. 4. Write an algorithm to compute the sample mean of a dataset. You should clearly specify the initialization, repeated steps, and output processing