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Question 1) (30 points + 10 points bonus) Chegg is an educational web site having the following vision statement "We strive to improve the overall return on investment in education by helping students learn more in less time and at a lower cost". The site also provides a honor code for academic integrity. On the other side, Lancester and Cotarlan (2021) report that students use Chegg for exam style questions. In specific disciplines, the student requests increased around 200% from 2019 to 2020. The company considers to redesign the locations of the servers in order to provide reasonable service to all ethically correct requests while decreasing the company costs. Five candidate locations are determined. Based on previous data, the demand is considered as 3 regions. The demand of each region, the capacity and annual operating cost of each candidate location as well as the cost of satisfying each unit of demand from each location are provided in Table 1. Table 1: Demand, Capacity and Cost Information for Question 1 Candidate locations Service Cost Per Demand Annual Capacity Annual Fixed Operating Costs B 1 9 2 2 4 18 1 14 10 1 12 200 2 7 1 90 3 6 8 80 4 3 3 7 120 4 5 16 130 Annual Demand 7 13 12 a) (30 points) Formulate an integer programming model for this problem to assist the company in determining which locations should be selected and how the demand of each region will be satisfied in order to minimize total cost of fixed and service costs. You can express your model in open or closed form. Do not forget to define sets, parameters, decision variables, objective function and constraints. You don't need to suggest a solution. You are not expected to solve the problem on GAMS. b) (Bonus: 10 points) Define the following constraints to your model: i. (2 points) At most three locations can be opened ii. (2 points) If location 1 is opened then location 2 should be opened as well. iii. (3 points) If location 3 is opened it must serve at least 10 units of demand. iv. (3 points) Locations 4 and 5 belong to the same firm. The firm does not accept to operate only one of these locations. Either both will be opened or none