BM 58700/GSLM 53000
Operations Research I
Fall 10/11
Assignment #8
#1.
Define LP P as:
max z = 3x1 + 4x2 + x3,
s.t.
x1 + 2x2 + 2x3
3x1 + x2 + x3
x1, x2, x3 ≥ 0.
≤ 12,
≤ 16,
(a).
Solve LP P by Simplex method.
(b).
Find LP D, the dual of LP P.
(c).
Find the complementary solution for each BFS of LP P identified in tableaus of (a).
(d).
For the pairs of complementary solutions found in (c):
(i).
verify that they satisfy the complementary slackness conditions;
(ii).
check that the solutions for LP D satisfy the optimality condition but are infeasible;
(iii). graph the constraints and the feasible region of LP D, and trace the locations of the
complementary solutions of LP D on the graph.
(e). Solve LP D by Dual Simplex method. Compare the basic solutions in the Dual
Simplex tableaus with the complementary solutions found in (c).
#2.
Define LP P1 as:
max z = 3x1 + 4x2 + x3,
s.t.
x1 + 2x2 + 2x3
3x1 + x2 + x3
x1, x2, x3 ≥ 0
≥ 12,
≤ 16,
(a).
Solve LP P1 by the two-phase method.
(b).
Solve LP P1 by the general primal-dual procedure.