** Please do not copy from from other solutions and please read the question carefully.

The Southwest National Bank is working to develop 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, employee breaks, and so on. The number of tellers necessary to provide adequate customer service during each hour of operation is summarized in the following table.

Time	Number of Teller	Time	Number of Teller
9:00 am 10: 00 am	6	2:00 pm 3: 00 pm	6
10:00 am 11: 00 am	4	3:00 pm 4: 00 pm	4
11:00 am 12: 00 pm	8	4:00 pm 5: 00 pm	7
12:00 pm 1: 00 pm	10	5:00 pm 6: 00 pm	6
1:00 pm 2: 00 pm	9	6:00 pm 7: 00 pm	6

Each full-time employee starts on the hour and works a 4-hour shift, followed by 1 hour for lunch and then a 3-hour shift. Part-time employees work one 4-hour shift beginning on the hour. Considering salary and fringe benefits, full-time employees cost the bank $105 a day, and part-time employees cost the bank $32 per day.

a) Formulate a linear programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum employee cost and answer the following questions in the algebraic formulation sheet.

b) After reviewing the solution to part a, the bank manager realized that some additional requirements must be specified. Specifically, she wants to ensure that one full-time employee is always on duty and that there is a staff of at least five full-time employees. Also, total number of part-time employees for 6:00 pm- 7:00 pm cannot be more than 1/3 of full-time employees in this time period. Write new constraints to incorporate these additional requirements & Formulate a linear programming model