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Unformatted text preview: CO 350 MIDTERM EXAM Thursday, February 11, 2010 1. [marks: 11=6+5] (a) Consider the following linear programming problem ( P ): max x 1 − 2 x 2 subj. to 2 x 1 + x 2 − x 3 ≤ 8 4 x 2 + 2 x 3 = 12 − x 1 + 5 x 2 ≤ 20 x 2 , x 3 ≥ Write down the dual problem of ( P ). Do not apply any transformation to ( P ); start from the given ( P ) and obtain ( D ) directly. (b) Consider the following linear programming problem ( Q ): min − x 1 + 2 x 2 subj. to 2 x 1 + x 2 − x 3 ≤ 8 4 x 2 + 2 x 3 = 12 − x 1 + 5 x 2 ≤ 20 − 2 x 1 + 3 x 2 + x 3 ≥ 3 x 2 ≥ x 3 ≤ Convert ( Q ) to standard equality form. 2. [marks: 11=2+1+6+2] Consider the following feasible tableau ( T 1 ) for a maximization linear programming problem: z + 2 x 1 − x 2 − 4 x 5 = 2 − 4 x 1 + 2 x 2 + x 3 − 2 x 5 = 1 x 1 − 2 x 2 + 3 x 5 + x 6 = 12 6 x 2 + x 4 + x 5 = 4 1 (a) What is the basic solution x * determined by ( T 1 )? (b) What is the objective function value of x * ? (c) Give all the choices of pairs ( x k ,x r ) that are possible combinations for entering variable ( x k ) and leaving variable ( x r ) in the next iteration of the simplex method applied to ( T 1 ). Clearly indicate which variable is entering and which variable is leaving. Do)....
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This note was uploaded on 05/28/2011 for the course CO 250 taught by Professor Guenin during the Fall '10 term at Waterloo.
 Fall '10
 GUENIN

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