The hospital administrator at Community General Hospital must appoint head nurses to four newly established departments: urology, cardiology, orthopedics, and obstetrics. In anticipation of this staffing problem, she had hired four nurses: Hopkins, Berry, Clooney, and Estephan. Believing in the decision modeling approach to problem solving $($i$.$e$.,$ prescriptive analytics$),$ the administrator has interviewed each nurse, considered his or her background, personality, and talents, and developed a scale ranging from $0$ to $50$ points rating to be used in the assignment.

A $50$ for a Nurse being assigned to the cardiology unit implies that the nurse would be perfectly suited for that task. A value close to $0,$ on the other hand, would imply that the nurse is not at all suited to head that unit. The table below gives the complete set of the rating figures that the hospital administrator felt represented all possible assignments. Which nurse should be assigned to which unit?

$\backslash$table$[[,$Department$],[$Nurse$,$Urology,Cardiology,Orthopedics,Obstetrics$],[$Hopkins$,30,28,20,48],[$Berry$,32,38,23,38],[$Clooney$,33,38,24,36],[$Estephan$,25,40,38,15]]$

a$.$ Define the decision variables of this problem.

b$.$ Provide the algebraic formulation of the objective function.

c$.$ Formulate this problem as an $$Assignment Model$$ on a spreadsheet and use Excel$$s Solver to determine which nurse should be assigned to which unit and the optimal rating. $($Provide the corresponding $$Excel Spreadsheet$$ and the $$Answer Report$).$ Include $$managerial statements$$ that communicate the results of the analyses $($i$.$e$.$ describe verbally the results$).$