$(60$ points$)$ You are a supervisor assigning people to different jobs. Every person must perform at least one job and can perform at most three jobs. Job $2$ requires two people. Every job must be done. Anyone doing job $3$ cannot do job $2$ or $5.$ The table below provides the cost of assigning each individual to each job.

$\backslash$table$[[$Person$/$Job$,1,2,3,4,5],[1,12,10,5,8,9],[2,10,7,6,10,6],[3,8,4,5,8,7]]$

a$)(20$ points$)$ Create an IP to optimize this problem.

b$)(20$ points$)$ Solve your model using MS Excel or CPLEX.

c$)(20$ points$)$ Design a hill climbing algorithm to find the solution of your model $($write all of the steps$).$ Show two steps of your model.