solution

The Hills County, Michigan, superntendent of education is responsible for assigning students to the three high school in This county He recognizes the need to but a camber of students for several sectors, A-E of the county are beyond walking distance to a school. The superiodu pon the county into geographic sector tempts to establish a plan trust wil ze heftalmber of student miles aveled by bus He also recognizes that student happens to be a tan sector and is signed to the high school in the sector, there is no need to be him because he can walk to school. There wchools are located in sectors B, C and E. The accomparing tabletes the umber of high-school-age students vingineach sector de la centrom each odor to each school Distance to School Sector School in Sector School in Sector School in Sector Number of E Students 00 000 20 1.000 700 SYD A 12 0 O 12 Each schon 1200 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 Distance to School Sector School in Sector School in Sector School in Sector B ? E A 7 5 6 B 0 4 12 ? 4 0 7 D 5 4 7 E 12 7 0 Total Number of Students 800 600 400 1,000 700 3,500 Each high school has a capacity of 1,200 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 sector. The number of decision variables for the model = 15 a) The objective function, for the LP model Minimize Z v +5 V +6 + XEB XAB Each high school has a 00 students You have been asked 1 XDB ar programming Decision variable X;;: ! The number of decision XCB . nts living in sector e model = 15 a) The objective functio XBB »del = Minimize Z= 7 + 5 + 6 + ??? XEC Each high school has a capacity SW Xool You have been asked to develop aming mo XBC n sector Decision variable X;;: Number of The number of decision variables 15 xpc a) The objective function, for the Minimize Z= 7 + 5 + 6 + XBE XEE Each high school has a capacity of 1,200 s You have been asked to develop a linear pi ??? Decision variable Xij. Number of students ! The number of decision variables for the m XDE a) The objective function, for the LP model ??? Minimize Z = 7 + 5 V + 6 +