$\backslash$table$[[$SCORE$,30,35,35,100]]$

$[30$ pts$.]$ Four workers are available to perform four jobs. The time it takes each worker to perform each job is given in the following table. The goal is to assign workers to jobs so as to minimize the total time required to perform the four jobs.

a$)$ Write the mathematical model. b$)$ Use the Hungarian method to solve the problem.

$\backslash$table$[[,$Time$($hours$)],[,$Job $1,$Job $2,$Job $3,$Job $4],[$Worker $1,4,7,8,6],[$Worker $2,6,9,4,7],[$Worker $3,8,5,3,9],[$Worker $4,7,6,7,5]]$

$x_1=1,x_2=1,x_3=1,x_4=1,$ and $z=$

$q,$