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# assignment2 - 0 T(b[1 1 1 0 T(c 1 3[11-2-5 T(d 1 6[17-3-2-5...

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ORIE 3300/5300 ASSIGNMENT 2 Fall 2011 Individual work. Due: 11am, Tuesday September 13. 1. Consider the simple Sudoku-style puzzle below. You must ﬁll each cell with one of the four numbers 1, 2, 3, or 4. (Four of the cells are already ﬁlled.) 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 ﬁle (with comments!) and output. 2. For the system of equations x 1 + x 2 - x 3 + 4 x 4 = 1 x 2 - 2 x 3 - x 4 + x 5 = - 1 x 1 + x 3 + x 5 = 2 which of the following is a basic solution? Justify your answers. (a) [2 , - 1 ,

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Unformatted text preview: , , 0] T ; (b) [1 , 1 , 1 , , 0] T ; (c) 1 3 [11 , , ,-2 ,-5] T ; (d) 1 6 [17 ,-3 , ,-2 ,-5] T ; 1 3. Consider the set of vectors x satisfying x 1 + 3 x 2 + 2 x 3 + x 4 = 4 2 x 1 + 6 x 2 + 5 x 3 + x 4 = 9 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. (d) Find a feasible solution that is not an extreme point: justify your answer by using the deﬁnition of extreme point. 2...
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assignment2 - 0 T(b[1 1 1 0 T(c 1 3[11-2-5 T(d 1 6[17-3-2-5...

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