Consider the trivial separable program min 21x - 322 s.t. 0 … x … 6

(a) Verify that the model is a convex program.

(b) Verify by inspection that an optimal solution occurs at x* = 3.

(c) Form a linear programming approximation 17.61 using u0 = 0, u1 = 2, u2 = 6.

(d) Solve your LP approximation of part (c)

by inspection, and determine whether correctness condition 17.62 is satisfied by the approximate optimum.

(e) Discuss how convexity of part

(a) relates to correct sequencing 17.62 in part (d).

(f) Verify by inspection that x* = 0 and x* = 6 are alternative optima in the original NLP when the objective is maximized instead of minimized.

(g) Repeat part (d), this time maximizing the objective function.

(h) Comment on the errors introduced in objective function and other values when sequencing condition 17.62 is violated in part (g).