Answer Happy

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 mles from each sector to each school a) The objective function, for the LP model= Minimize Z 5 XAB+XAC+6XAE 0X88 4Xec 12 X XBE 4Xce +0Xcc +7XCE Xos+2 Xoc+5XDE 12 Xee 7Xec OXEE Subject to XABXAC XA XenXec Xee +Xce- Distance to School Sector School in Sector School in Sector School in Sector B E XcB Xos XocXDE Xee+Xect XAD A 8 D Total 5 0 4 7 $1,000 1,000 12 Each high school has a capacity of 1,000 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 number of students in sector A number of students in sector B number of students in sector C number of students in sector D number of students in sector E 1,000 8 school B capacity school C capacity school E capacity 6 non negativity condition 12 7 0 Number of Students 750 600 150 800 500 2.800 For all X, 20 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)