Question 3 [16 points] A local government approved establishing a national standard metrology and quality organization. Its main activities include formulation and approval of national standards for all commodities and products as well as standards concerned with metrology, calibration, marking and identification of commodities and products, methods of sampling, inspection, and testing, in addition to other assignments. The facility should consist of two multi floors buildings where each building consists of 5 floors. The area of each floor is measured in m2, and denoted by Sg. Also, the distance in meters between any consecutive floors is . The initial plan is to open 18 main departments in the organization which are listed in the table below: The flow between any two of departments, say i and j, is given as fij with flow cost is cij. The company is seeking your help to determine the allocation of the above departments into the two buildings. 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) Each department must be assigned to only one floor and one building b) The sum of areas of all departments in a floor should be less than Sg. c) Departments 1 to 9 should be assigned in one building, and departments 10 to 18 are in another building. d) If Electrical products Laboratory is not assigned to floor 3 in building 2, then Petroleum Products Laboratory should not be assigned to floor 5 in building 1 . e) If Finance Department is assigned to any floor or building, then departments 1, 2, 4 and 5 should be assigned to the same building and floor. f) If Chemical Laboratory, Vehicles inspection unit, and Laboratories of the First Industrial Zone are assigned to either building, then they should be in different floors. g) In either building, on the first floor, Km2 of space is required for security and safety. h) The labs departments can not all be assigned to the same building