$1.$ As in the previous project, we will express solutions by giving the assigned locations of our $5$

respective departments. For this project, our initial assignment is $5-3-2-4-1,$ which means that

the first department is assigned to location $5,$ the second to location $3,$ the third to location $2$ and

so forth. This initial solution is given both in red in cells C$5$ G$5$ and in black in cells C$4$ G$4$

in the project spreadsheet; it has an objective function value of $4361,$ which we see in cell H$2.$

The previous project introduced local search as a good technique for improving on any initial

solution. As before, we define a current solution$$s neighbors as solutions found by swapping the

locations of two of its departments. For example, the first neighbor of our starting solution

would swap locations of departments $1$ and $2,$ giving the solution $3-5-2-4-1.($Now department $1$

is given location $3,$ while department $2$ gets location $5.)$ The sequence $3-5-2-4-1$ would be

entered in cells C$4$ G$4$ on the project template, which would then give the objective function

value for this neighbor in cell H$2.$ Investigate each of the $10(5$C$2)$ neighbors that can be created

by swapping any pair of departments. To do this, perform one swap at a time, writing down its

objective function in the following table, and then return to the original $($or current$)$ solution after

each swap. The first $2$ neighbors are filled in $($though not their objective function values$).$ For

convenience, the current solution $5-3-2-4-1$ is stored in red so that it$$s easy to get back to it after

investigating each neighbor.