assignment2_ProblemSet

assignment2_ProblemSet - (b[0 1-2 2 0 T(c[0 1 1 0 T(d 1 2[1...

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ORIE 3300/5300 ASSIGNMENT 2 Fall 2008 Individual work. Due: 3 p.m., Friday September 19. 1. Consider the simple Sudoku-style puzzle below. 3 2 4 You must fll each cell with one oF the Four numbers 1, 2, 3, or 4. (±our oF the cells are already flled.) Each oF the Four numbers appears exactly once in each row, exactly once in each column, and exactly once in each oF the Four bold squares. Solve the puzzle by hand. Then solve the problem again using AMPL. Include your model fle (with comments!) and output. 2. ±or the system oF equations 2 x 1 + 4 x 3 - x 4 - 2 x 5 + x 6 = 2 x 1 + x 2 + x 4 + 2 x 5 + x 6 = 2 2 x 2 + x 4 + 2 x 5 + x 6 = 2 which oF the Following is a basic solution? JustiFy your answers. You may want to perForm some elementary row operations to help you. (a) [1 , 1 , 0 , 0 , 0 , 0] T ;

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Unformatted text preview: (b) [0 , , 1 ,-2 , 2 , 0] T ; (c) [0 , , 1 , , 1 , 0] T ; (d) 1 2 [1 , 1 , , , , 2] T ; 1 3. Consider the set of vectors x satisfying 3 x 1 + 6 x 2 + 8 x 3 + x 4 = 7 x 1 + 2 x 2 + 4 x 3 + x 4 = 3 x 1 , x 2 , x 3 , x 4 ≥ . Answer the following questions, justifying your answers carefully. (a) Find an extreme point of the feasible region. (b) Find a basic solution that is not feasible. (c) Find a feasible solution that is not basic: justify your answer by using the de±nition of basic solution. (d) Find a feasible solution that is not an extreme point: justify your answer by using the de±nition of extreme point. 2...
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• Fall '08
• TODD
• feasible solution, Elementary matrix, elementary row operations, basic solution, extreme point, simple Sudoku-style puzzle

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assignment2_ProblemSet - (b[0 1-2 2 0 T(c[0 1 1 0 T(d 1 2[1...

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