A new branch of Rajhi Bank to open 24/7 in Makkah. The branch is large enough to accommodate up to 70 tellers. Although Management wishes to hire only part time tellers who are cheaper, they are forced by the regulations of the central bank SAMA -Saudi Arabian Monetary Agency- not have more than 30% part timers. Number of tellers needed depends on the provided expected number of customers during the time periods of the day. It is the bank policy to have at least one tellers for every 10 customers.

Period # Time Period Expected Customers

1 08- 10 240

2 10- 12 380

3 12- 14 450

4 14- 16 600

5 16- 18 340

6 18- 20 440

7 20- 22 660

8 22- 24 540

9 24- 02 260

10 02- 04 150

11 04- 06 460

12 06- 08 200

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The full-time tellers are paid SR30/hour and work 8 consecutive hours. They may start at 8:00AM, 4:00PM, and 12:00 Midnight. The part-time tellers are paid only SR20/hour and work 4 consecutive hours. They may start at 8:00AM, 12:00 Noon, 4:00PM, 8:00PM, 12:00 Midnight, or at 4:00AM.

You are consulted to provide a recommendation as to the number fulltime and part time tellers needed throughout the day to minimize the total daily cost. Additionally, provide the number of full-time and part-time tellers to be scheduled in every period of the day.

Formulate a decision making mathematical model to help answering the questions that will follow:

Hint: Let

F1 = Number of full-time tellers who start working at 08:00AM

F2 = Number of full-time tellers who start working at 16.00 Hour = 4:00PM

F3 = Number of full-time tellers who start working at Midnight

P1 = Number of part-time tellers who start working at 08:00AM

P2 = Number of part-time tellers who start working at 12:00Noon

P3 = Number of part-time tellers who start working at 16:00 Hours = 4:00PM

P4 = Number of part-time tellers who start working at 20:00 Hours = 8:00PM

P5 = Number of part-time tellers who start working at 24:00 Hours = 12:00Midnight

P6 = Number of part-time tellers who start working at 4:00AM

1. Write down an objective function that will minimize the total daily costs of the tellers.
2. Write down all constraints related to the branch capacity to accommodate tellers.
3. Write the constraint related to the SAMA regulation.
4. Write down all the constraints related to meeting the required number of tellers needed
5. Write down any other required constraints but not mentioned above.