Question $3(25$ points$)$

Nurses in a large hospital work $3$ days a week. The possible work schedules and the weekly wage paid to a nurse for each schedule are given in the following table. For a given schedule, if there is a $"x"$ sign on a given day, that means the nurse following that schedule works on that day. The other days are off$-$days. Each nurse works according to one schedule.

$\backslash$table$[[$Schedule Type,$],[$Day$,1,2,3,4,5,$Number of Nurses Required$],[$Monday$,$X$,,$X$,,,20],[$Tuesday$,$X$,,,,$X$,25],[$Wednesday$,,,$X$,$X$,,26],[$Thursday$,,$X$,,,$X$,26],[$Friday$,,$X$,,$X$,$X$,30],[$Saturday$,,$X$,,$X$,,30],[$Sunday$,$X$,,$X$,,,35],[$Weekly wage $($$$),525,470,550,500,425,]]$

$2$

The number of nurses needed for each day of the week are given in the last column.

$($a$)(15$ points$)$ Formulate an integer programming model to determine the total number of nurses required to meet the nurse requirements for each day at minimum cost. Define your decision variables clearly.

$($b$)(10$ points$)$ Solve the model you developed in part $($a$)$ using OpenSolver and report the optimal solution. Upload the excel file as well when uploading your solutions. $($Hint: Optimal objective function value is $$35,725)$