Problem $2.$ This question gives one example of the kinds of problems you can solve with max

flow models. Suppose you have four jobs that must be processed; the following table gives their

characteristics $($all times in hours$).$

Each job can be processed on any of three identical machines; to be finished, a job must be

processed for its entire processing time, but this processing can be interrupted and even moved to

a different machine if necessary. For example, we could process job $1$ from hour $2$ to $3$ on

machine $1,$ then pause it$,$ then process it from hour $4$ to $5$ on machine $2.$ However, you can't

"double$-$up$"$ and process a job simultaneously on two machines.

Formulate a maximum flow model that decides whether the jobs can be scheduled on the three

machines so that each job begins processing on or after its release time and ends processing no

later than its due time. $($Hint: Your network should have a node for every job, but also nodes for

intervals of time that represent machine processing capacity.$)$