Consider the following flow matrix:

For the above flow matrix, design a good row layout using the greedy approach considering an initial

layout of $1-2-3-4-5.$ Execute at most three full iterations of the greedy heuristic. $($Note: If a local optimal

solution is obtained before completing three iterations, then the algorithm can be terminated.$)$

Consider the typical layout given in the following figure:

a$.$ Construct a slicing tree representation of the layout given in the above figure.

b$.$ Develop a matrix representation of the layout given in the above figure.

c$.$ In the matrix representation developed in part $($b$),$ propose a change that will lead to swapping

department $5$ and department $7.($Swap type$-1)$

The following two parts $($d and e$)$ and not related to the above figure:

d$.$ Is the following slicing representation a valid representation? Explain

e$.$ Build the corresponding layout for the slicing representation given in part $($d$).$