Consider the linear program min 2x1 + 3x2 + 4x3 s.t. x1 + 2x2 + x3 3 2x1 - x2 + 3x3 4

Consider the linear program min 2x1 + 3x2 + 4x3 s.t. x1 + 2x2 + x3 Ú 3 2x1 - x2 + 3x3 Ú 4 x1, x2, x3 Ú 0

(a) Use nonnegative surplus variables x4 and x5 to place the model in standard form.

(b) State the dual of your standard form model in part

(a) in terms of variables v1 and v2.

(c) Choosing x4 and x5 as basic, compute the corresponding primal basic solution and establish that it is not feasible.

(d) Show that v1 = v2 = 0 is dual feasible in the standard form and complementary with the primal solution of part (c).

(e) Starting from the primal basis of part (c)
and dual solution of part (d), apply Dual Simplex Algorithm 6A to compute optimal primal and dual solutions for the given LP.