$1)$ Reapply the greedy algorithm we discussed today for the set covering problem with the function i$($f$\_\{$i$\},$ k$\_\{$i$\})=$ f$\_\{$i$\}-$ k$\_\{$i$\}$ and compare the results with what we did in clas. $2)$ Consider the Maximal Covering Problem. Develop the formulation in MS Excel and solve the model using the Excel Solver add$-$in$.$ You can refer to the Excel file we developed in class $($available in Teams$).$

$3)$ Consider the Set Covering Problem with Penalty Cost. Develop the formulation in MS Excel and solve the model using the Excel Solver add$-$in$.$ You can refer to the Excel file we developed in class.

a$)$ Take the p$\_\{$j$\}$ values as they are.

b$)$ Take the p$\_\{$j$\}$ values divided by ten.

c$)$ Take the p$\_\{$j$\}$ values divided by a hundred.

Note: Sample problem data $($also used in class$)$ for questions $2$ and $3$ are as follows:

t ij $=\backslash$table$[[$tij $($in km$,1\mathrm{.}2\mathrm{.}3\mathrm{.}4\mathrm{.}5.$

$1.133972$

$2.4514110$

$3.112645$

$4.185123$

hij $=[5060755590]$

pij $=[10003000250015002000]$