Consider the LP min 4x1 - x2 + 2x3 s.t. 4x1 - 3x2 + 2x3 = 13 3x2 - x3 = 1 x1, x2, x3 Ú 0

(a) Show that x102 = 13, 1, 22 is an appropriate point to start barrier Algorithm 7B.

(b) Form the corresponding log barrier problem with multiplier m = 10.

(c) Compute the move direction x that could be pursued from x102 by barrier Algorithm 7B. (See Table 7.4 for the projection matrix required.)

(d) Verify that your direction of part

(c) is improving and feasible in the barrier model of part

(b) at x102.

(e) Determine the maximum step lmax from x102 that preserves feasibility in your direction of part

(c) and the l to be employed.

(f) Will the barrier objective function first increase, then decrease, or first decrease, then increase, as the step l applied to your direction of part

(c) grows from 0 to lmax? Explain.

(g) The next time that multiplier m is changed, should it increase or decrease? Explain.