Amining company is going to continue operating in a certain area for the next 5 years. There are 10 mines in this area and the annual operating cost of mineX in year is currently all mines are operating, however, from now on, the company can operate at most 8 in any one year in order to we a mine operated in a certain year, the mine should be open in that year. If a mine is shut down in a year it cannot be operated in that year and in the following years within the five year horizon. There is a cost of shutting down a mine in year t, denoted by Si There is an upper limit to the amount of one which can be extracted from each mine in a year Maximum yearly output from mine tis C The ore are sold each year and price per ton is Pin yeart Below are the parameters and the relevant decision variables Brameters madrum yearly output from mines Pselling price of each ton of ore in yeart Rothe annual operating cost of mine in year Se the cost of shutting down a mine in yeart, Decalon walles X. Output obtained from mine in year tontona) Mit mine in operated in year and otherwise Notitie is shut down in year and otherwise Models that you formulate in all parts should be linear (YOU WILL NOT GET POINTS IF YOU HAVE NONLINEARITY CAUSED BY MULTIPLYING DECISION VARIABLES) Formulare a med integer programming model that made the profit by determining which mines should be operated each year and how much they should producer Explain the constraints in your model (Use the above decision variables, do not define any additional decision variables) in each of the cases below, make the necessary modifications in your model to represent the descritual situation. Defire any additional variables you may weed and enten.be modified parts of your model You are not allowed to change the variables defined in part (a). Consider cach case independently If mines 12, and are open in a given year, then yines and cannot be open in the same year If mines and are operated in the same year, then at most 90% of their total maximum yearly output can be obtained in that year, Amining company is going to continue operating in a certain area for the next 5 years. There are 10 mines in this area and the annual operating cost of mineX in year is currently all mines are operating, however, from now on, the company can operate at most 8 in any one year in order to we a mine operated in a certain year, the mine should be open in that year. If a mine is shut down in a year it cannot be operated in that year and in the following years within the five year horizon. There is a cost of shutting down a mine in year t, denoted by Si There is an upper limit to the amount of one which can be extracted from each mine in a year Maximum yearly output from mine tis C The ore are sold each year and price per ton is Pin yeart Below are the parameters and the relevant decision variables Brameters madrum yearly output from mines Pselling price of each ton of ore in yeart Rothe annual operating cost of mine in year Se the cost of shutting down a mine in yeart, Decalon walles X. Output obtained from mine in year tontona) Mit mine in operated in year and otherwise Notitie is shut down in year and otherwise Models that you formulate in all parts should be linear (YOU WILL NOT GET POINTS IF YOU HAVE NONLINEARITY CAUSED BY MULTIPLYING DECISION VARIABLES) Formulare a med integer programming model that made the profit by determining which mines should be operated each year and how much they should producer Explain the constraints in your model (Use the above decision variables, do not define any additional decision variables) in each of the cases below, make the necessary modifications in your model to represent the descritual situation. Defire any additional variables you may weed and enten.be modified parts of your model You are not allowed to change the variables defined in part (a). Consider cach case independently If mines 12, and are open in a given year, then yines and cannot be open in the same year If mines and are operated in the same year, then at most 90% of their total maximum yearly output can be obtained in that year