$3\mathrm{.}2$ At a machine tool plant, five jobs must be completed each day. The time it takes to do each job depends on the machine used to do the job, but not every machine can handle every job. If a machine is used at all, there is a $($one$-$time only$)$ setup time required. The relevant times $($in minutes$)$ are given below.

Each machine can handle at most two jobs per day, and in addition, since machines $1$ and $2$ require the same people to do setup, an additional $20$ minutes is needed if both machines are used. Determine how to minimize the sum of the setup and machine operation times needed to complete all jobs.

$"$No need to solve the problem, only give the mathematical formulations"!!!!!!