You are required to plan the weekly schedule for a medical clinic. The clinic works 7 days a week, in three shifts; the first shift is between 08:00 AM-4:00 PM, the second between 4:00 PM-12:00 AM, and the third between 12:00 AM and 08:00 AM. The experiences and the wages of the 10 employees are given in Table 1. In the second shift (4:00 PM-12:00 AM), at least one employee with minimum 3 years of experience should be present. In the third shift (12:00 AM and 08:00 AM) at least one employee with minimum 6 years of experience should be present. In each shift, at least three employees should be working.

The availability of the employees for the following week is given in Table 2. In developing the schedule, we additionally have the following constraints: - Each person should be working at least 5 and at most 8 shifts a week. - A person cannot work on two shifts on the same day. - The novices Aysu and Erhan cannot be assigned together to any of the shifts. (a) Develop a mathematical formulation for this problem. Define all your decision variables and constraints clearly. (b) Solve the model using an optimization solver (Excel, OPL, etc.)

Table 1. Employee Information 48 Employee Experience Wage ($) per shift Aysu 1 year 24 Bahar 5 years 42 Can 7 years Deniz 4 years 40 Erhan 1.5 years 27 Gamze 15 years 58 lgi 2.5 years 32 Koray 45 Lale 51 Tugay 2 years 30 6 years 8 years Table 2: Availability of Employees Employee Aysu Bahar Can Deniz Erhan Gamze lgi Koray Lale Tugay Monday S1* S2* S3* Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Availability Tuesday Wednesday Thursday Friday Saturday Sunday S1 S2 S3 S1 S2 S3 Si S2 S3 S1 S2 S3 S1 S2 S3 S1 S2 S3 Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes *S1: 08:00 AM-4:00 PM S2: 4:00 PM12:00 AM S3: 12:00 AM-08:00 AM