Problem $3(20$ points$).$ A machine tool plant owns four different machines $on$ which $it$ can process jobs. $If$ a machine $is$ used $at$ all, then a setup time $is$ needed. A job cannot $be$ divided between machines, that $is$ each job must $be$ processed $by$ exactly one machine. Note however that one machine can process more than one job. The relevant times $in$ minutes are given $in$ the following table. The goal $isto$ minimize the sum $of$ the setup and machine operation times

needed $to$ complete all $4$ jobs. Moreover, $itis$ required that $if$ machine $2$ and machine $3$ are both set $up,$ then job $2$ should not $be$ assigned $to$ machine $2.$

Formulate $a(mixed-)integer$ linear optimization model for the machine tool plant. Use computer tools $to$ find $an$ optimal solution $to$ this model.