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examsp01 - 15.053 Midterm Tuesday, March 12, 2001 (closed...

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15.053 Midterm Tuesday, March 12, 2001 (closed book ) 1. Answer all questions in exam books provided. 2. Budget your time. If a problem (or a part of a problem) is taking too long, you may want to go on to the next one. 3. If you think that there is an ambiguity on a question, please state the assumption you are making. (Try to make the assumption reasonable.) 4. The exam sums to 105 points.
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1. (60 points, 5 points per part). z x 1 x 2 x 3 x 4 x 5 x 6 RHS -1 0 w 1 0 0 w 2 * 3 (0) 0 0 w 3 1 0 * * 7 (1) 0 0 w 4 0 1 * * 4 (2) 0 1 w 5 0 0 * * w 6 (3) The above problem is a maximization problem. For parts a to g, we ask you below to provide conditions on w 1 , w 2 , … w 6 for your answers. Please ignore all values labeled “*”, even though those values are also unknown. You do not need to specify values of an unknown if it is not relevant. For example, there is no need to specify the value of w 3 for part a. a. Under what condition on the unknown values is the current basic solution feasible? b. Under what condition on the unknown values is the current solution feasible and degenerate? c. Assuming that the current basis is feasible, what is the basic feasible solution? Give the values of all of the decision variables as well as the objective value. The solution and objective value can be stated in terms of w 6 if necessary. d. Under what conditions on the unknown coefficients is the current solution optimal? (You may assume it is feasible.) e. Suppose that the solution is feasible but not optimal and that variable x 2 is next pivoted into the basis. Under what conditions is the solution unbounded from
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This note was uploaded on 12/20/2011 for the course BUS 15.053 taught by Professor Prof.jamesorlin during the Spring '05 term at MIT.

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examsp01 - 15.053 Midterm Tuesday, March 12, 2001 (closed...

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