Consider the work scheduling model we covered in this chapter.

Part a$)$ Rewrite the objective function in a way that the total wage paid to the security

staff is explicitly minimized. The hourly wage is assumed to be $$17.$

Note: Make sure to take the duration of each shift into account.

Part b$)$ Add a constraint that ensures the combined number of staffs starting at $8$ pm$,$

midnight, and $4$ am does not exceed $35\%$ of the total number of staffs.

Next Step:

The above $($modified$)$ version of the scheduling problem $($including the constraints

from the original version$)$ was entered in MPL$.$ Refer to the screenshot of the $*.$sol

$($output$)$ file on the next page. Based on the output, answer parts c$-$e $($below$)$:

Part c$)$ What is the optimal assignment of the security staff to the shifts? Explain what

it means.

Part d$)$ Given the optimal solution in $($c$),$ calculate the total wage to be paid over a

$24-$hour period.

Part e$)$ Identify the shadow price corresponding to each constraint. Compare the

values for time windows $(1,3,5)$ with those of $(2,4,6).$ What can you conclude?