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# hw2 - IE521 Advanced Optimization HW2 Due November 16 Fall...

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IE521 Advanced Optimization HW2 Due November 16 Fall 2011 1. In a school trip there are students with age 7 to 17. The average age of the students is 14. Give an LP formulation in order to ﬁnd the minimum number of students who are older than 14 years-old. Give an LP formulation in order to ﬁnd the maximum number of students who are younger than 10 years-old. 2. Bertsimas 2.3 Consider the polyhedron deﬁned by the constraints Ax = b and 0 x u . Assume that the matrix A has linearly independent rows and that u > 0. Provide a procedure for constructing the basic solutions. 3. Consider the following linear program. min - 16 x 1 - 14 x 2 - 15 x 3 - 50 x 4 (1) s.t. 2 x 1 + 2 x 2 + 5 x 3 + 16 x 4 800 (2) 3 x 1 + 2 x 2 + 2 x 3 + 5 x 4 1000 (3) 2 x 1 + 1 . 2 x 2 + x 3 + 4 x 4 680 (4) x 1 ,x 2 ,x 3 ,x 4 0 (5) (a) Construct an initial tableau. (b) Which variables are the basic variables? What is the basic solution? (c) If you enter

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hw2 - IE521 Advanced Optimization HW2 Due November 16 Fall...

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