Consider the standard-form LP min 10x1 + 1x2 s.t. x1 - x2 + 2x3 = 3 x2 - x3 = 2 x1, x2, x3 Ú 0

(a) Show that x102 = 14, 3, 12 is an appropriate point to start affine scaling Algorithm 7A.

(b) Derive the associated scaled standard form corresponding to solution x102.

(c) Compute the move direction x that would be pursued from x102 by Algorithm 7A

(refer to Table 7.4 for projection matrices).

(d) Show that your direction is improving and feasible at x102.

(e) Compute the step size l that Algorithm 7A would apply to your direction, and determine the new point x112 that results.