Consider the standard-form linear program max 5x1 - 10x2 s.t. 1x1 - 1x2 + 2x3 + 4x5 = 2 1x1 + 1x2 + 2x4 + x5 = 8 x1, x2, x3, x4, x5 Ú 0

(a) Taking x1 and x2 as basic, identify all elements of the corresponding partitioned model: B, B-1, N, cB, cN, and b.

(b) Then use the partitioned elements of part

(a) to compute the primal primal basic solution 1xB, xN2, determine its objective value, and establish that it is feasible.

(c) Formulate the dual of the above LP in terms of partitioned elements of part (a)

and dual variables v.

(d) Compute the complementary dual solution vQ corresponding to the basis of (a), and verify that its objective value matches that of the primal.

(e) Briefly explain how your complementary primal and dual solutions x and vQ can have the same objective function value yet not be optimal in their respective problems.