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Unformatted text preview: University of California, Davis Department of Agricultural and Resource Economics We are what we repeatedly do. Excellence then is not an act, but a habit. Aristotle Copyright c 2011 by Quirino Paris. ARE 155 Winter 2011 Prof. Quirino Paris HOMEWORK #8 Due Tuesday, March 1 1. State the rules for using 1. the primal simplex algorithm; 2. the dual simplex algorithm; 3. the artificial variable algorithm. For each algorithm, you must describe three steps: step 0, step 1 and step 2. 2. Consider the following LP problem: max Z = 3 x 1 + 4 x 2 + 5 x 3 + 2 x 4 subject to x 1 + 2 x 2 + 3 x 3 + 4 x 4 12 2 x 1 + x 2 + 5 x 3 + 4 x 4 18 x j , j = 1 , . . . , 4 . A) Solve the above LP problem using the appropriate algorithms. B) Exhibit the complete optimal primal and dual solutions as well as the optimal primal and dual bases. C) Using the information in the optimal tableau, compute the opportunity cost of commodity 4 evaluated at market prices and at factor costs. D) By how much should the objective function coecient for activity 4 increase in order to make that activity profitable? E) By how much should the objective function coecient for activity 2 increase in order to make that activity profitable? F) Verify that, in the optimal tableau, the product of the primal slack variables times the corresponding dual variables is always equal to zero. The same holds for the product of the dual slack variables times the corresponding primal variables. We have already discussed this property which is called complementary slackness and it is the subject of Chapter 9. Hence, read and study Chapter nine.it is the subject of Chapter 9....
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