Jawwal As-Sharq (JAS) is planning to build communication towers on any of the 6 available mountains in the eastern region. The cost of building tower on any mountain in thousand riyals is given as Bm, where m=1,,6. After building the tower, JAS has to decide what should be the capacity (kWh) and height (mts) of the tower. The capacity and height of the tower decides the range for a tower. For example: for any tower, A capacity +B height will be equal to range (sqMts), where A and B some well known constants. Moreover, there will be operating costs of Cm thousand riyals per unit tower capacity, and Hm thousand riyals per unit tower height. ASJ would like to build the towers with the following requirements: - ASJ wants to select exactly 2 mountain sites in total. - Towers should not be build on both Mountain 6 and 9. - The range is zero before building tower. - If range of Mountain-5 is above 33 sqMits, then range of Mountain-6 should be above 47 sqMits. - If range of tower in Mountain-1 is less than or equal to 42sqM,s, then the range of tower on Mountain 2 or 3 (or both) should be above 49 sqMits. - ASJ wants to minimize the total cost of building and operating the towers. Answer the following questions: 1. Define the variable(s) that can be used for modeling the above scenario. 2. Write the mathematical model explicitly that captures the above restrictions. (You are free to use additional variables/parameters. Define the additional variables/parameters clearly.) Jawwal As-Sharq (JAS) is planning to build communication towers on any of the 6 available mountains in the eastern region. The cost of building tower on any mountain in thousand riyals is given as Bm, where m=1,,6. After building the tower, JAS has to decide what should be the capacity (kWh) and height (mts) of the tower. The capacity and height of the tower decides the range for a tower. For example: for any tower, A capacity +B height will be equal to range (sqMts), where A and B some well known constants. Moreover, there will be operating costs of Cm thousand riyals per unit tower capacity, and Hm thousand riyals per unit tower height. ASJ would like to build the towers with the following requirements: - ASJ wants to select exactly 2 mountain sites in total. - Towers should not be build on both Mountain 6 and 9. - The range is zero before building tower. - If range of Mountain-5 is above 33 sqMits, then range of Mountain-6 should be above 47 sqMits. - If range of tower in Mountain-1 is less than or equal to 42sqM,s, then the range of tower on Mountain 2 or 3 (or both) should be above 49 sqMits. - ASJ wants to minimize the total cost of building and operating the towers. Answer the following questions: 1. Define the variable(s) that can be used for modeling the above scenario. 2. Write the mathematical model explicitly that captures the above restrictions. (You are free to use additional variables/parameters. Define the additional variables/parameters clearly.)
