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Unformatted text preview: Problem 1. Assuming that the x i ’s are decision variables and all other symbols are constant, determine whether each of the following is a linear program. (a) min 3 x 1 7 x 2 + 4 x 3 s.t. 3 X i =1 h i x i = 3 ≤ x i ≤ 4 , i = 1 , 2 , 3 Answer: YES . (b) min 3 /x 1 4 x 2 s.t. x 1 + x 2 ≥ x 3 x i ≥ , i = 1 , 2 , 3 Answer: NO . (c) min 200 X i =1 x i / ( σ 2 i ) s.t. 100 X i =1 α i x i ≤ 200 X i =101 α i x i x i ≥ , i = 1 , 2 , ··· , 200 Answer: YES . (d) min 2 x 1 4 x 2 s.t. x 2 1 + x 2 ≥ 4 x i ≥ , i = 1 , 2 Answer: NO . (e) min 3 x 1 + 6 x 2 + 4 x 3 s.t. x 1 x 2 ≥ 2 x 3 x i ≥ , i = 1 , 2 , 3 x 3 integer Answer: NO . 1 Problem 2. Consider the following linear program max 3 x 1 + x 2 s.t. x 1 + x 2 ≥ 2 4 x 1 + x 2 ≥ 4 x 1 x 2 ≤ 1 x 1 + 2 x 2 ≤ 4 x 1 3 x 2 ≤ (a) Solve above linear program using graphical method. (b) If the objective function becomes x 1 + 3 x 2 , solve the problem again. (c) If the objective function becomes x 1 x 2 , solve the problem again, do we still have just one optimal solution? (d) Does the feasible region change if we drop the constraint x 1 3 x 2 ≤ 0?...
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This note was uploaded on 08/31/2010 for the course IESE GE 330 taught by Professor Nedich during the Spring '09 term at University of Illinois at Urbana–Champaign.
 Spring '09
 Nedich

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