Question 3 [14 points]: IHCC is a specialized healthcare construction company signed a project contract to build a new hospital in Dhahran City. The new hospital is multi-floor facility consisting of 8 floors where g = 1, 2, ... 8. The area of each floor is measured in m, and denoted by Sg. Also, the distance in meters between any consecutive floors is 8. The initial plan is to open 14 main departments in the hospital which are listed in the table below: Department Department Department Name Number Department Name Number 1 Accident and emergency (A&E) 8 Chaplaincy 2. Admissions 9 Intensive Care Unit (ICU) 3 Anesthetics 10 Pharmacy 11 Breast Screening Diagnostic Imaging 4 12 Burn Center Human Resources 5 13 General Services 6 Cardiology Central Sterile Services 14 Finance Department 7 (CSSD) The area of department i is A; m?, and the flow between any two of the departments, say i and j, is given as fij with flow cost cij. The company is seeking your help to determine the allocation of the above departments into the 8 floors. Write a full formulation of the following problem statements after you define your variables and parameters (if any) clearly: (note: each question part is independent of others) a) Assume the possible departments that can be assigned to the first floor are four departments, namely (A&E), Admissions, Pharmacy, and Diagnostic Imaging. Write only a linear objective function that minimizes the cost per unit time for movement among the departments. b) The total areas of the departments which are planned to be assigned to the first floor and given in part (a) should not exceed 1220 m2. c) If Anesthetics department is assigned to floor g, then Cardiology, and Chaplaincy departments can not be assigned to the same floor. He donament should b) The total areas of the departments which are planned to be assigned to the first floor and given in part (a) should not exceed 1220 m2. c) If Anesthetics department is assigned to floor 9, then Cardiology, and Chaplaincy departments can not be assigned to the same floor. d) If (ICU) is assigned to floor 7, then the General Services department should be assigned to flow 4. e) The vertical distance between Admissions and (ICU) must be 28 mts. f) If it is planned to assign Human Resources department to any floor such that g2, then departments of General Services and Finance should be assigned to the adjacent floors (i.e. not both of them on the same adjacent floor). g) If departments of (A&E), Admissions, and Pharmacy are assigned to the first floor, then Diagnostic Imaging department should be assigned to the same floor. h) On the first floor, K m of space is required for security and safety. i) If Ll: A; > L9=1 Sg, then what can be concluded about the assignment problem? Question 3 [14 points]: IHCC is a specialized healthcare construction company signed a project contract to build a new hospital in Dhahran City. The new hospital is multi-floor facility consisting of 8 floors where g = 1, 2, ... 8. The area of each floor is measured in m, and denoted by Sg. Also, the distance in meters between any consecutive floors is 8. The initial plan is to open 14 main departments in the hospital which are listed in the table below: Department Department Department Name Number Department Name Number 1 Accident and emergency (A&E) 8 Chaplaincy 2. Admissions 9 Intensive Care Unit (ICU) 3 Anesthetics 10 Pharmacy 11 Breast Screening Diagnostic Imaging 4 12 Burn Center Human Resources 5 13 General Services 6 Cardiology Central Sterile Services 14 Finance Department 7 (CSSD) The area of department i is A; m?, and the flow between any two of the departments, say i and j, is given as fij with flow cost cij. The company is seeking your help to determine the allocation of the above departments into the 8 floors. Write a full formulation of the following problem statements after you define your variables and parameters (if any) clearly: (note: each question part is independent of others) a) Assume the possible departments that can be assigned to the first floor are four departments, namely (A&E), Admissions, Pharmacy, and Diagnostic Imaging. Write only a linear objective function that minimizes the cost per unit time for movement among the departments. b) The total areas of the departments which are planned to be assigned to the first floor and given in part (a) should not exceed 1220 m2. c) If Anesthetics department is assigned to floor g, then Cardiology, and Chaplaincy departments can not be assigned to the same floor. He donament should b) The total areas of the departments which are planned to be assigned to the first floor and given in part (a) should not exceed 1220 m2. c) If Anesthetics department is assigned to floor 9, then Cardiology, and Chaplaincy departments can not be assigned to the same floor. d) If (ICU) is assigned to floor 7, then the General Services department should be assigned to flow 4. e) The vertical distance between Admissions and (ICU) must be 28 mts. f) If it is planned to assign Human Resources department to any floor such that g2, then departments of General Services and Finance should be assigned to the adjacent floors (i.e. not both of them on the same adjacent floor). g) If departments of (A&E), Admissions, and Pharmacy are assigned to the first floor, then Diagnostic Imaging department should be assigned to the same floor. h) On the first floor, K m of space is required for security and safety. i) If Ll: A; > L9=1 Sg, then what can be concluded about the assignment