• Problem 1 Suppose that an LP has the following set of...

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IE 310 Operations Research First Midterm Exam Fall 2015 Name: UIN: There are four problems. You have 50 minutes to finish and submit your solution. Please write neatly. Problem 1 a 3 pt b 3 pt c 4 pt Problem 2 a 2 pt b 2 pt c 4 pt d 3 pt Problem 3 a 4 pt b 4 pt c 2 pt d 3 pt Problem 4 a 2 pt b 2 pt c 2 pt d 3 pt e 3 pt Total 46pt 1
(0.5,b+1.5) (1.5,b+1.5) (1,b+1) (1,b+2) Problem 1. Suppose that an LP has the following set of constraints, as is shown by the above feasible region ( b is some positive constant). x 1 + x 2 b + 3 x 1 + x 2 b + 2 - x 1 + x 2 b + 1 - x 1 + x 2 b ( a ) [3pt] determine the optimal solution x * = ( x * 1 , x * 2 ) and the optimal objective value Z * if the objective function is maximize x 1 + 2 x 2 ( b ) [3pt] determine the optimal solution x * = ( x * 1 , x * 2 ) and the optimal objective value Z * if the objective function is maximize - 2 x 1 + x 2 ( c ) [4pt] consider the following LP. Determine which constraint should be removed in order to make the Dual LP infeasible . (The Dual LP is infeasible if it has an empty feasible region.) maximize x 1 + x 2 subject to x 1 + x 2 b + 3 (constraint 1) x 1 + x 2 b + 2 (constraint 2) - x 1 + x 2 b + 1 (constraint 3) - x 1 + x 2 b (constraint 4)

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