Answer the following questions with reference to feasible regions formed by a system of linear inequalities in two variables.
a. (i) Define (a) a feasible region and (b) a vertex (corner point) of a feasible region.
b. (ii) Explain, with reasoning, why every optimal value of a linear objective function (if it exists) must occur at a vertex of the feasible region.
c. (iii) Coincident constraint lines may reduce the number of distinct vertices of the feasible region. Describe how this happens and illustrate your explanation with a symbolic example (no sketch required).