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Please assist me with the below: The bank is working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide

Please assist me with the below:

The 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. On Fridays, the bank is open from 9:00 A.M. to 7:00 P.M. The number of tellers necessary to provide adequate customer service during each hour of operation is summarized here.

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Each full-time employee starts on the hour and works a 4-hour shift, followed by a 1-hour break 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 $15 per hour ($105 a day), and part-time employees cost the bank $8 per hour ($32 per day).

Formulate an integer programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum employee cost. (Hint: Let xi = number of full-time employees coming on duty at the beginning of hour i and yj = number of part-time employees coming on duty at the beginning of hour j.)

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xi, yj 0 and integer for i = 9, 10, 11 and j = 9, 10, 11, 12, 1, 2, 3

(b) Solve the LP Relaxation of your model in part (a).

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(d) After reviewing the solution to part (c), the bank manager realized that some additional requirements must be specified. Specifically, she wants to ensure that one full-time employee is on duty at all times and that there is a staff of at least four full-time employees. Revise your model to incorporate these additional requirements, and solve for the optimal solution.

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Time 9:00 a.m.-10:00 a.m 10:00 a.m.-11:00 a.m 11:00 a.m.-Noon Noon-1:00 p.m. 1:00 p.m.-2:00 p.m No. of Tellers Time 2:00 p.m.-3:00 p.m 3:00 p.m.-4:00 p.m 4:00 p.m.-5:00 p.m 5:00 p.m.-6:00 p.m 6:00 p.m.-7:00 p.m. No. of Tellers 8 4 8 8 4 10 9 10

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