For the LP in K&B Section 3.2, problem 11 (converted to K&B canon- ical form), consider the basis B {x1, X3, X4}. Perform the following steps: (a) Write the problem in partitioned matrix form, i.e., write В, N, b, св, Cм, хв, and xv. (b) Find B-1. (c) Compute the corresponding basic primal solution xB = B-'b, xN O and the objective value, z. (d) Compute the corresponding dual basic solution wT cB-l and the objective value z'. (e) Verify that the two solutions are feasible and satisfy complementary slackness. What do you conclude about the prob- lem. 4 is an optimal solution to the linear Suppose that x = 2, x2 0, x3 programming problem %3D Maximize z = 4x, + 2x2 + 3x3 subject to 2.x, + 3x2 + x,< 12 X + 4x2 + 2x3 s 10 3x, + x2 + x3 s 10 x, z 0, x2 2 0, x3 2 0. Using the principle of complementary slackness and the duality theorem (Theorem 3.7), find an optimal solution to the dual problem. What value will the objective function of the dual problem have at this optimal solution?

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