IEOR162_SampleMidterm2

# IEOR162_SampleMidterm2 - Department of Industrial...

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IEOR162 Linear Programming SAMPLE Midterm Exam 2 Fall 2011 Name: SAMPLE Midterm Exam 1 Grade: SAMPLE Midterm Exam 1 1. Consider the following linear program max x 1 - 2 x 2 s.t. x 1 + 2 x 2 - x 3 2 x 1 - x 2 3 x i 0 i = 1 , 2 , 3 . Write down the standard form of the program (with no artiﬁcial variable) and then ﬁnd all the basic solutions of your standard form LP. For each basic solution, determine whether it is a basic feasible solution or not. 1

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2. (25 points) Consider the following linear program max x 1 + 3 x 2 + x 3 + x 4 s.t. x 1 + x 2 - 2 x 3 6 2 x 1 - 3 x 2 + x 4 ≤ - 9 3 x 2 - 2 x 3 - x 4 = 3 x i 0 i = 1 ,..., 4 . Use the big-M method and follow the smallest index rule to determine the feasibility of this program. Either ﬁnd a feasible solution or show that the problem is infeasible. 2
3. When you use the simplex method to solve a maximization LP, suppose you get a tableau c 1 c 2 0 0 3 0 10 4 a 1 1 0

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IEOR162_SampleMidterm2 - Department of Industrial...

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