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# hw1 - IE521 Advanced Optimization HW1 Due October 26 Fall...

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IE521 Advanced Optimization HW1 Due October 26 Fall 2011 1. Draw the graphical representation of the following linear programming model: x 1 + 8 3 x 2 + x 3 = 4 (1) x 1 + x 2 + x 4 = 2 (2) 2 x 1 + x 5 = 3 (3) x 1 , x 2 , x 3 , x 4 , x 5 0 (4) 2. Find the bacis solutions defined by the constraints (1) - (4). Which are these solutions are basic feasible solutions? 3. Bertsimas 1.9 Consider a school district with I neighborhoods, J schools, and G grades at each school. Each school j has a capacity of C jg for grade g . In each neighborhood i , the student population of grade g is S ig . Finally, the distance of school j from neighborhood i is d ij . Formulate a linear programming problem whose objective is to assign all students to schools, while minimizing the total distance traveled by all students. You may ignore the fact that number of students must be integer. 4. Bertsimas 1.10 A company must deliver d i 0 units of its product at the end of the i th month. In each month, the units produced by the company can either be delivered

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