Consider the mathematical program max 4z1 + 7z2 s.t. 2z1 + z2 … 9 0 … z1 … 4 0 … z2 … 3

(a) Show that directions  z112 = 12, 02 and

 z122 = 1 -2, 42 are improving directions for this model at every z.

(b) Beginning at z102 = 10, 02, execute Improving Search Algorithm 3A on the model. Limit your search to the two directions of part (a), and continue until neither is both improving and feasible.

(c) Show in a two-dimensional plot the feasible space and objective function contours of the model. Then plot the path of your search in part (b).