Question: Consider the three-variable linear programming problem shown in Fig. 5.2. (a) Explain in geometric terms why the set of solutions satisfying any individual constraint is

Consider the three-variable linear programming problem shown in Fig. 5.2.

(a) Explain in 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.

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