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ISyE 323 – Midterm Exam 2 - University of Wisconsin, Madison

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ISyE 323 – Midterm Exam 2 April 10, 2014. 2:30–3:45PM READ THIS! 1. This exam has a total of 10 pages. 2. The exam is closed book, and you are allowed to use one side of one sheet of notes. ... 3. Write your name on your note sheet and turn it in with your exam. 4. Please silence and put cell phones away. 5. The more clearly you write your answer, the better the chance that we can grade it accurately and give it full credit. 6. If you need more space, you may write on the back of the exam, but you must indicate on the front side of the page if you have done so. 7. For any true/false or multiple choice question that do not ask for an explanation, you may still optionally add an explanation. A correct answer will receive full credit with no explanation. An incorrect answer might receive partial credit, depending on the explanation. (I recommend adding optional explanations only if you have extra time.) 8. The number of points for each problem is displayed at the end of the problem’s title. The time required for Eric to complete each question is also listed. Please use your time wisely. Eric and I will collect all the papers promptly at 3:45. No extra time. 9. Good luck! Problem Points Eric Time (min.) 1 12 1.5 2 11 4.5 3 14 4 4 15 5 5 11 4.5 6 12 4 Total 75 23 Page 1 ISyE323 Midterm Exam 2 Name: 1 True or False Circle true or false. 1.1 (2 points) True or False: If the dual of a linear program is infeasible, then it is possible that the the primal linear program is also infeasible. 1.2 (2 points) True or False: For every basic solution of a linear program in standard form, there is a corresponding extreme point in the feasible region. 1.3 (2 points) True or False: When solving a linear program with the two-phase simplex method, the phase 1 linear program can never be unbounded. 1.4 (2 points) True or False: The greedy algorithm can be used to find the shortest path between two nodes in a network. 1.5 (2 points) True or False: In the simplex algorithm, if the minimum ratio obtained in the ratio test is zero, then the solution obtained after performing the simplex pivot will be the same as the current solution. 1.6 (2 points) True or False: If the shortest path from node 1 to node 8 in a network is 1 → 5 → 7 → 3 → 6 → 8, then the path 5 → 7 → 3 → 6 must be a shortest path from node 5 to node 6. 2 Multiple choice and short answer 2.1 (2 points) Suppose you have a linear program in standard form with n variables and m constraints and you choose any set of n − m variables and set their values to zero, and then attempt to solve for the other variables using the given equations. What will be the outcome of this process? (a) This will always yield a basic feasible solution. (b) This will always yield a basic solution. (c) This might yield a basic solution, or it might not yield a solution at all. Page 2 ISyE323 Midterm Exam 2 Name: 2.2 (3 points) Consider the linear program below: min z = 5x1+3x2 subject to: 2x1+3x2 ≥ 6 x1−2x2 ≤ 0 x1 ≥ [Show More]

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