Use GAMS$/$any coding language to solve the following problems. Sample data is provided. Submit your

GAMS$/$any coding language files with the solutions.

Consider the following total tardiness formulation. Solve this formulation using GAMS$/$any coding

language.

$mi{n}_k=1^n{t}_k$

subject $to$

${\displaystyle \underset{i=1}{\overset{n}{}}}{x}_{ik}=1$ for $k=1,$dots,$n$

${\displaystyle \underset{k=1}{\overset{n}{}}}{x}_{ik}=1$ for $k=1,$dots,$n$

${\displaystyle \underset{i=1}{\overset{n}{}}}(p_i{\displaystyle \underset{u=1}{\overset{k}{}}}{x}_{ii})-{\displaystyle \underset{i=1}{\overset{n}{}}}{d}_i{x}_{ik}{t}_k$ for $i,k=1,$dots,$n$

$x_{ik}in\{0,1\}$ fob $iis$ assigned $tokth$ position $in$ sequence

$t_k=$ tardiness $of$ job $k$

Now solve the problem in GAMS$/$any coding language by modifying the formulation so that your

objective function is minimizing total weighted completion time instead of minimizing total tardiness.

Solve the problem in GAMS$/$any coding language this time with the objective of minimizing the

total number of late jobs.

Submit three different GAMS$/$any coding language files $($zip them$).$

Sample data: