Consider the standard-form LP min 14z1 + 3z2 + 5z3 s.t. 2z1 - z3 = 1 z1 + z2 = 1 z1, z2, z3 Ú 0

(a) Determine the direction of most rapid objective function improvement at any solution z.

(b) Compute the projection matrix P for the main equality constraints.

(c) Apply your P to project the direction of (a).

(d) Verify that the result of part

(c) is improving and feasible at any interior point solution.

(e) Describe the sense in which the direction of part

(c) is good for improving search at any interior point solution.