Question $2.$ Oski University keeps a supercomputer for research use by its faculty, Ph$.$D$.$ students, and

research associates. During all working hours, an operator must be available to operate and maintain the

computer, as well as to perform some programming services.

It is now the beginning of the fall semester, and the head operator must devise a schedule that assigns

different employees to different time slots. There must be exactly one operator staffed on the supercomputer

Monday through Friday from $8$ am to $10$ pm$.$ Because all operators are students, they are only free to work

only a limited number of hours each day, as shown in the following table.

Employee Monday Tuesday Wednesday Thursday Friday

$160606$

$206060$

$348404$

$455505$

$530380$

$600062$

$($Assume that the employee$$s time can be split up into multiple shifts in one day, e$.$g$.,$ Employee $1$ can work

multiple short shifts on Monday, as long as the total time she works is less than $6$ hours$).$

The employees are paid at different rates due to variability in their experience:

Operator $123456$

Wage $($$$/$hr$)10\mathrm{.}0010\mathrm{.}109\mathrm{.}909\mathrm{.}8010\mathrm{.}8011\mathrm{.}30$

Finally, operators $1-4$ are each guaranteed to be staffed at least $8$ hours a week, and operators $5$ and $6$ are

guaranteed $7$ hours a week.

Formulate a linear programming model that minimizes total weekly staffing costs while ensuring that the

supercomputer is always staffed.