Consider the unconstrained NLP max x1x2 - 51x1 - 224 - 31x2 - 524

(a) Use graphing software to produce a contour map of the objective function for x1  [1, 4], x2  [2, 8].

(b) Compute the move direction that would be pursued by gradient search Algorithm 16D at x102 = 11, 32.

(c) State the line search problem implied by your direction.

(d) Solve your line search problem graphically and compute the next search point x112.

(e) Do two additional iterations of Algorithm 16D to compute x122 and x132.

(f) Plot progress of the search on the contour map of part (a).