Return to the LP and x102 of Exercise 7-15.

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

(b) Compute the move direction x that would be pursued from x102 by Algorithm 7B with m = 10 (refer to Table 7.4 for projection matrices).

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

(d) Compute the maximum step size lmax that can be applied to your direction of part

(b) at x102 without losing feasibility.

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