Workers at the Execo manufacturing plant work $5$ consecutive days a

week, e$.$g$.$ a worker can start work on a Monday and continue till Friday

while another can start work on a Wednesday and continue till Sunday

etc. Workers who are off on weekends $($Saturday and Sunday$)$ are paid

$$300$ per day $($for each of their $5$ work days$),$ workers who$$s schedules

involve one weekend day are paid $$320$ per day $($for each of their $5$ work

days$),$ and workers who$$s schedules involve both weekend days are paid

$$330$ per day $($for each of their $5$ work days$).$ The goal is to determine

the number of workers for each schedule to minimize cost subject to the

following restrictions:

$$ There must be at least $25$ workers each day.

$$ There can be at most $35$ workers on at least $3$ of the $7$ days of the

week.

$$ If the number of workers that start on a Monday exceed $10$ then the

number of workers available on a Wednesday should be no more than

$28.$

$$ The number of workers that start on a Saturday should be less than

the number of workers that start on a Monday or a Tuesday.

$$ A total $40$ workers are available.

Formulate the above problem as a mixed$-$integer linear problem. Use xi to

denote the number $($integer$)$ of workers who start work on day i$.$ You may

need to introduce additional binary variables. If you use big$-$M numbers,

please provide your best estimates of their values.