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Unformatted text preview: MS&E 211 Midterm Examination  Autumn 2007 Page 1 of 15 M IDTERM E XAMINATION MS&E 211 October 30, 2007 INSTRUCTIONS a) Take alternate seating if possible. b) This is an open book and open notes exam. You are not permitted to use computers or any calculator programming functions. c) Answer all questions on the exam. d) The examination ends in 75 minutes. e) There are 4 questions on this exam plus one bonus question. The exam is worth 100 points with an additional 15 bonus points available. HONOR CODE In taking this examination, I acknowledge and accept the Stanford University Honor Code. NAME (signed) NAME (printed) Pr. 1 Pr. 2 Pr. 3 Pr. 4 Bonus Total MS&E 211 Midterm Examination  Autumn 2007 Page 2 of 15 Problem 1 True or False (20 points) State whether each of the following italicized statements is True or False. Assume all other in formation given is correct. For each part, only your answer, which should be one of True or False, will be graded. Explanations will not be read. a) Consider the linear program: Minimize c T x subject to Ax = b x where x < n , A < m n and b < m . True or False: Assume that there are at least two different optimal solutions to this problem. Then there are at least two different basic feasible optimal solutions to this problem. b) Still consider the linear program above. True or False: Assume that there is at least one optimal solution to this problem and every optimal solution is a basic feasible solution. Then the problem has only one optimal solution. MS&E 211 Midterm Examination  Autumn 2007 Page 3 of 15 c) One can easily see that the linear program below is infeasible. Minmize x 1 2 x 2 subject to x 1  1 x 2  1 x 1 ,x 2 True or False: The dual problem is unbounded. d) Consider the following linear program: Maximize x 1 + x 2 subject to x 1 + x 2 3 x 1 x 2 x 1 x 1 ,x 2 True or False: The dual of the problem is infeasible for any MS&E 211 Midterm Examination  Autumn 2007 Page 4 of 15 Problem 2 Optimal Currency Conversion (25 points) You are currently planning a vacation to Greece for the fall break and must therefore convert some of your earned U.S. dollars into Euros. Assume that 3 currencies are available for doing your conof your earned U....
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