Consider the unconstrained NLP min max510 - x1 - x2, 6 + 6x1 - 3x2, 6 - 3x1 + 6x26

(a) Explain why Nelder–Mead search is appropriate for solving this unconstrained optimization.

(b) Do 3 iterations (moves) of Nelder–Mead Algorithm 16G, starting from initial ensemble

(5, 0), (10, 5), (5, 5).

(c) Plot the progress of your search through centroids x1t2 and connecting the 3 points of each ensemble with dashed lines.