Question $1(20$ marks$)$

You are Manager of an organisation and need to assign four jobs to four workers. Table Q$1$ below shows the cost of each worker to each job. Each worker can be assigned to one or two jobs. Th cost of workers has been recorded for different jobs, and you are required to allocate one worker for each job using the Hungarian Method in the most cost$-$effective way.

$\backslash$table$[[,$Job$],[$Worker$,$No $1,$No $2,$No $3,$No $4],[$A$,4,12,9,11],[$B$,2,10,3,8],[$C$,8,5,6,11],[$D$,4,15,13,9]]$

Table Q$1-$ Cost of Workers to Jobs

$($a$)$ Briefly describe the type of problem that this is$.$

$(2$ marks$)$

$($b$)$ Convert the cost matrix to an appropriate form for using the Hungarian Method. What is the optimal solution?

$(6$ marks$)$

$($c$)$ If Job No $1$ cannot be assigned to Worker B$,$ and Worker C can only take Job No $2$ or Job No $3,$ what is the optimal solution now?

$(6$ marks$)$

$($d$)$ If Table Q$1$ above also gives the profit of each job, what is the optimal solution?

$(6$ marks$)$