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QUESTION #3: [12 Marks] Consider a town with four elementary schools (A, B, C and D). The school board has implemented a series of standards of learning (SOL) tests in reading, math, and history that all schools are required to administer to all students in the fifth grade. The average tests scores are a measurable output of the schools performance. The school board has identified three key resources (i.e. inputs) that affect a school's SOL scores: The teacher-to-student ratio, supplementary funds per student (i.e. funding generated through donations and other private sources over and above the normal budget), and the average educational level of the parents (where 12 = high school graduate, 16 = college graduate, etc.). The inputs and outputs are summarized as follows: Input 1 = teacher-to-student ratio Input 2 = supplementary funds per student Input 3 = average educational level of parents Output 1 = average reading SOL score Output 2 = average math SOL score Output 3 = average history SOL score The actual input and output values for each school are: School A 1 0.06 Inputs 2 $260 3 11.3 1 86 Outputs 2 75 3 71 B 0.05 320 10.5 82 72 67 0.08 340 12.0 81 79 80 D 0.06 460 13.1 81 73 69 For example, at school A, the teacher-to-student ratio is 0.06 (or approximately 1 teacher per 16.67 students), there is $260 per student supplemental funds, and the average parent educational grade level is 11.3. The average scores in reading, math, and history for school A are 86, 75, and 71, respectively. The school board wants to identify the school or schools that are less efficient in converting their inputs to outputs relative to the other elementary schools in the town. 4 MSCI-3200 QDM II a) Develop a DEA linear programming model that can be used to evaluate the performance of School D only. State your model in algebraic form by clearly defining your decision variables and by giving quantitative expressions for the constraints and the objective function in terms of the data and decisions. (5) b) Use the Excel Solver to solve the model. What is the optimal solution and the value of the objective function? Note: Do not submit a spreadsheet. (3) c) Is School D efficient or inefficient? Discuss. (1) d) Where does the composite school have more output than School D and by how much? (1) e) How much less of each input resource does the composite school require when compared to School D? (1) f) What other schools should be studied to find suggested ways for School D to improve its efficiency? (1) QUESTION #3: [12 Marks] Consider a town with four elementary schools (A, B, C and D). The school board has implemented a series of standards of learning (SOL) tests in reading, math, and history that all schools are required to administer to all students in the fifth grade. The average tests scores are a measurable output of the schools performance. The school board has identified three key resources (i.e. inputs) that affect a school's SOL scores: The teacher-to-student ratio, supplementary funds per student (i.e. funding generated through donations and other private sources over and above the normal budget), and the average educational level of the parents (where 12 = high school graduate, 16 = college graduate, etc.). The inputs and outputs are summarized as follows: Input 1 = teacher-to-student ratio Input 2 = supplementary funds per student Input 3 = average educational level of parents Output 1 = average reading SOL score Output 2 = average math SOL score Output 3 = average history SOL score The actual input and output values for each school are: School A 1 0.06 Inputs 2 $260 3 11.3 1 86 Outputs 2 75 3 71 B 0.05 320 10.5 82 72 67 0.08 340 12.0 81 79 80 D 0.06 460 13.1 81 73 69 For example, at school A, the teacher-to-student ratio is 0.06 (or approximately 1 teacher per 16.67 students), there is $260 per student supplemental funds, and the average parent educational grade level is 11.3. The average scores in reading, math, and history for school A are 86, 75, and 71, respectively. The school board wants to identify the school or schools that are less efficient in converting their inputs to outputs relative to the other elementary schools in the town. 4 MSCI-3200 QDM II a) Develop a DEA linear programming model that can be used to evaluate the performance of School D only. State your model in algebraic form by clearly defining your decision variables and by giving quantitative expressions for the constraints and the objective function in terms of the data and decisions. (5) b) Use the Excel Solver to solve the model. What is the optimal solution and the value of the objective function? Note: Do not submit a spreadsheet. (3) c) Is School D efficient or inefficient? Discuss. (1) d) Where does the composite school have more output than School D and by how much? (1) e) How much less of each input resource does the composite school require when compared to School D? (1) f) What other schools should be studied to find suggested ways for School D to improve its efficiency? (1)