Question: 3. (Duality, Complementary slackness). Consider the following simple linear pro- gram: (min)/(:1) = -2.11 - 22 s.t. 2 + x2 0. (a) Write the dual

3. (Duality, Complementary slackness). Consider

3. (Duality, Complementary slackness). Consider the following simple linear pro- gram: (min)/(:1) = -2.11 - 22 s.t. 2 + x2 0. (a) Write the dual of this linear program. 4 marks (b) By inspection, determine all basic feasible solutions to the dual. Which of these solutions are optimal? (Be sure your stated solutions are solutions to the dual of the LP in the form given. Changing the LP to an equiv- alent form may change the sign of the dual solution.) EXPLAIN YOUR METHOD 7 marks (c) Using complementarity arguments, determine the optimal primal solution. SHOW YOUR WORK. 7 marks (d) Is the dual solution y = WORK. (2,0,0) dual feasible? Why? SHOW YOUR 2 marks

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