This includes but is not limited to copying or sharing answers on tests or

# This includes but is not limited to copying or

This preview shows page 1 - 3 out of 3 pages.

Regulations and will not be tolerated. This includes, but is not limited to: copying or sharing answers on tests or assignments, plagiarism, having someone else do your academic work or working with someone on homework when not permitted to do so by the instructor. Depending on the act, a student could receive an F grade on the test/assignment, F grade for the course, and could be suspended or expelled from the University. See the Conduct Code at for more details and a full explanation of the Academic Misconduct policies. 1
1. (5 points) Prove that if (i) x is feasible to max { c > x : Ax b, x 0 } , (ii) y is feasible to min { b > y : A > y c, y 0 } , and (iii) c > x = b > y , then x and y are both optimal. 2. (5 points) Prove that exactly one of the following two alternatives holds for the LP max { c > x : Ax 0 , x 0 } : (a) x * = 0 is an optimal solution, (b) LP is unbounded. 3. (10 points) Find the dual of the following LP using the primal-dual table without reformu- lation. Solve both primal and dual LPs using a computer solver, and check the optimality condition to verify the optimality of the solutions. Please submit (1) the dual LP, (2) primal optimal solution and optimal objective value, (3) dual optimal solution and optimal objective value, (4) optimality condition, (5) whether or not the optimal solutions satisfy the optimality condition. max x 1 + 2 x 2 s . t . x 1 - 2 x 2 - x 3 + x 4 0 4 x 1 - 3 x 2 + 4 x 3 - 2 x 4 3 - x 1 + x 2 + 2 x 3 + x 4 = 1 x 2 0 , x 3 ≥ - 1 .

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• Spring '12
• lizhiwang