The Dublin branch of the ACE Bank is located in a local Safeway store. The branch manager is working on developing an efficient work schedule for full-time and part-time tellers. The schedule must provide for efficient operation of the bank including adequate customer service, teller breaks, and so on. The bank is open daily from 9 a.m. to 7 p.m. The number of tellers necessary to provide adequate customer service during each hour of operation is summarized in the table below:

Each full-time teller starts on the hour and works a four-hour shift, followed by one hour of a non-paid lunch, and then a three-hour shift. Part-time tellers work one four-hour shift beginning on the hour. Considering salary and fringe benefits, a full-time teller coststhe bank $30 per hour, and a part-time teller costs the bank $18 per hour. Questions. 1. Formulate an integer programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum total daily cost. 2. Solve the model using Excel Solver for the optimal schedule of tellers. Present the optimal schedule and comment on the solution. 3. After reviewing the solution in question 2, the bank manager has realized that some additional requirements must be incorporated into the schedule. Specifically, she wants to ensure that two full-time tellers are on duty at all time periods and that there is a staff of at least six full-time tellers working daily. Revise the model to incorporate these additional requirements. Present the new constraints in a mathematical form and incorporate them into the spreadsheet model. Solve the revised model, present the new schedule, and comment on the solution. 4. When finished with the revised model, the manager has realized again that she forgot one more requirement. According to the contract with the bank union, the number of full-time tellers per day should be at least 45% of the total number of full- and part-time tellers per day. Revise the model again, solve it, and present the new schedule. Comment on this solution and compare this solution with the previous two solutions in terms of the number of full-and part-time tellers and total daily cost. 5. For the optimal model in question 4, develop an example of one-way and two-way sensitivity analysis (one example of each) using SolverTable for a parameter(s) of your choice. Present and briefly explain the results of your sensitivity analysis (use separate worksheets for each type of sensitivity analysis).

\begin{tabular}{|c|c|c|c|c|} \hline Time & Numberoftellers & & Time & NumberofTellers \\ \hline 910am & 4 & & 23pm & 4 \\ \hline 1011am & 3 & & 34pm & 4 \\ \hline 11am12pm & 3 & & 45pm & 5 \\ \hline 121pm & 6 & & 56pm & 5 \\ \hline 12pm & 6 & & 67pm & 4 \\ \hline \end{tabular}