$1.[25$ pts$.]$ Five workers are available to perform five 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 five jobs. Use the Hungarian method to solve the problem.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline & $\backslash$multicolumn$\{6\}\{|$c$|\}\{$ Time$($hours$)\}\backslash \backslash$

$\backslash$cline $\{2-6\}$ & Job $1$ & Job $2$ & Job $3$ & Job $4$ & Job $5\backslash \backslash$

$\backslash$hline Worker $1$ & $6$ & $12$ & $3$ & $11$ & $15\backslash \backslash$

$\backslash$hline Worker $2$ & $4$ & $2$ & $7$ & $1$ & $10\backslash \backslash$

$\backslash$hline Worker $3$ & $8$ & $11$ & $10$ & $7$ & $11\backslash \backslash$

$\backslash$hline Worker $4$ & $16$ & $19$ & $12$ & $23$ & $21\backslash \backslash$

$\backslash$hline Worker $5$ & $9$ & $5$ & $7$ & $6$ & $10\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$