You are required to plan the weekly schedule for a medical clinic. The clinic works 7 days a week, in three shifts; 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 PM12:00 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. Table 1. Employee Information Employee Experience Wage ($) per shift Aysu 1 year 24 Bahar 5 years Can 7 years Deniz 4 years Erhan 1.5 years Gamze 15 years 2.5 years Koray 6 years Lale 8 years Tugay 2 years ilgi 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 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. Table 2: Availability of Employees EmployeeM onday S1 S2 S3 Aysu Yes Yes Bahar Yes Yes Can Yes Yes Deniz Yes Erhan Yes Yes Gamze Yes Yes Ilgi Yes Yes Koray Yes Lale Yes Yes Yes Tugay Yes Availability Tuesday Wednesday Thursday Friday Saturday Sunday S1 S2 S3 S1 S2 S3 S1 S2 S3 S1 S2 S3 S1 S2 S3 S1 S2 S3 Yes Yes 1 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 YesYes 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 You are required to plan the weekly schedule for a medical clinic. The clinic works 7 days a week, in three shifts; 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 PM12:00 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. Table 1. Employee Information Employee Experience Wage ($) per shift Aysu 1 year 24 Bahar 5 years Can 7 years Deniz 4 years Erhan 1.5 years Gamze 15 years 2.5 years Koray 6 years Lale 8 years Tugay 2 years ilgi 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 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. Table 2: Availability of Employees EmployeeM onday S1 S2 S3 Aysu Yes Yes Bahar Yes Yes Can Yes Yes Deniz Yes Erhan Yes Yes Gamze Yes Yes Ilgi Yes Yes Koray Yes Lale Yes Yes Yes Tugay Yes Availability Tuesday Wednesday Thursday Friday Saturday Sunday S1 S2 S3 S1 S2 S3 S1 S2 S3 S1 S2 S3 S1 S2 S3 S1 S2 S3 Yes Yes 1 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 YesYes 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