# Question: After deciding to close one of its middle schools the

After deciding to close one of its middle schools, the Springfield school board needs to reassign all of next year’s middle school students to the three remaining middle schools. Many of the students will be bused, so minimizing the total busing cost is one objective. Another is to minimize the inconvenience and safety concerns for the students who will walk or bicycle to school. Given the capacities of the three schools, as well as the need to roughly balance the number of students in the three grades at each school, how can linear programming be used to determine how many students from each of the city’s six residential areas should be assigned to each school? What would happen if each entire residential area must be assigned to the same school?

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Describe graphically what the simplex method does step by step to solve the following problem. Minimize Z = 5x1 + 7x2, Subject to and x1 ≥ 0, x2 ≥ 0. Consider the augmented form of linear programming problems that have feasible solutions and a bounded feasible region. Label each of the following statements as true or false, and then justify your answer by referring to ...Suppose that the three-variable linear programming problem given in Fig. 5.2 has the objective function Maximize Z = 3x1 + 4x2 + 3x3. Work through the matrix form of the simplex method step by step to solve the model given in Prob. 4.1-5. Most of the description of the fundamental insight presented in Sec. 5.3 assumes that the problem is in our standard form. Now consider each of the following other forms, where the additional adjustments in the ...Post your question