Consider the standard-form LP max 13w1 - 2w2 + w3 s.t. 3w1 + 6w2 + 4w3 = 12 w1, w2, w3 Ú 0

(a) Sketch the feasible space in a plot like Figure 7.6, identify an optimal extreme point, and show w112 = 11.4, 0.7, 0.92 and w2 = 10.01, 0.01, 2.97752.

(b) Form the corresponding log barrier problem with multiplier m 7 0.

(c) Using m = 10, evaluate the original and log barrier objective functions at w112 and w122. Then comment on the effect of barrier terms at points far from the boundary versus ones near the boundary.

(d) Use the class optimization software to solve log barrier form

(b) with multipliers m = 100, 10, and 1.

(e) How does the trajectory of optimal solutions to part

(b) evolve as mS 0?