Please I need help to formulate on mixed- integer problem 1-decision variables (binary or normal) 2-objectives functions 3-constraints (no need for numerical solution) Question 1 (30 pts) There are a total of 8 different districts in Muscat. The municipality of Muscat wants to build fire stations to some of these districts so that in case of an emergency every district can be reached within 15 minutes. The following matrix provides the distance between the districts in terms of minutes. 1 - N 15 1 2 3 4 5 6 7 8 18 10 20 3 12 257 33 17 21 28 40 20 22 11 | 12 30 22 3 17 22 24 10 35 4 5 5 15 30 22 6 42 10 7 5 8 In order to build a fire station to a district, an initial investment cost of s is required. The fire stations can be built in different capacities. An installation cost of ci is incurred per each unit capacity. . (10 pts) Formulate a mixed integer linear programming formulation that decides on the locations of the fire stations and their capacities in order to minimize the total cost. Write the following constraints or objective functions. Each part is independent of the others. Unless stated otherwise, all constraints are hard constraints. If a constraint/objective function is not linear, use appropriate techniques to linearize it: a. (2 pts) Total established capacity must be at least K units. b. (2 pts) If a fire station is established in district 1, there cannot be a fire station neither in district 4. c. (2 pts) If a fire station is established in district 2, a district must also be established in district 6. d. (2 pts) Either the capacity of district 1 must be larger than or equal to 10 or the capacity of district 2 must be less than or equal to 50. e. (2 pts) If a fire station is established in district 3, there must be fire stations in at least two of the districts 1, 5, 6, and 8