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The Hills County, Michigan, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, for several sectors, A-E, of the county are beyond walking distance to a school. The superintendent partitions the county into five geographic sectors as he attempts to establish a plan that will minimize the total number of student miles traveled by bus. He also recognizes that if a student happens to live in a certain sector and is assigned to the high school in that sector, there is no need to bus him because he can walk to school. The three schools are located in sectors B, C, and E. The accompanying table reflects the number of high-school-age students living in each sector and the distance in miles from each sector to each school: Sector School in Sector B 5 0 Sector C A B C D F Total Distance to School School in School in Sector E 6 4 12 0 7 2 0 Number of Students 700 500 100 800 400 2.500 5 7 12 Each high school has a capacity of 900 students. You have been asked to develop a linear programming model so as to minimize the total number of student miles traveled by bus. Decision variable X;;: Number of students living in sector i traveling to school located in sectorj. The number of decision variables for the model = 0 a) The objective function, for the LP model = Minimize Z= 5 XAB +8 XAC +6 XAE 4Xgc + 12 XBE 4Xce +0Xcc 0 XBB The number of decision variables for the model = 1 a) The objective function, for the LP model = Minimize Z= XAB +8XAC +6 XAE 0 XB8 +4 XBc +12XBE 4 Xce +0Xcc +7XCE 7 XDB +2 XDC +5 XDE 12 XER+7lXec +OXEE Subject to: XAB+XAC+XAE = 700 number of students in sector A XBe +Xgc +Xge - 500 number of students in sector B Xce +Xcc + Xce=100 number of students in sector C Xpe+Xoc+XDE 800 number of students in sector D XEB+Xec XEE - 400 number of students in sector E XAB XBB Xcs + XDB school B capacity Xc : Xec Xcc | school C capacity XCE XDE school E capacity For all Xij 20 non negativity condition b) Using a computer software for solving LP, the objective value at the optimal solution achieved is: Minimum number of total miles traveled objective value) = (round your response to a whole number). Xocl X===900 XEc5900 XEE 5900 XAE - BE Enter your answer in each of the answer boxes