Consider the following problem.

Maximize Z 3x1  4x2  2x3, subject to x1  x2  x3 20 x1  2x2  x3 30 and x1  0, x2  0, x3  0.

Let x4 and x5 be the slack variables for the respective functional constraints. Starting with these two variables as the basic variables for the initial BF solution, you now are given the information that the simplex method proceeds as follows to obtain the optimal solution in two iterations: (1) In iteration 1, the entering basic vari n geometric terms why the set of solutions satisfying any individual constraint is a convex set, as defined in Appendix 2.

(b) Use the conclusion in part

(a) to explain why the entire feasible region (the set of solutions that simultaneously satisfies every constraint) is a convex set.