Mathematics

Problem

The parameter

a \in \mathbb{R}

appears in the following system of inequalities:

x + y \le 6

y \ge 2x + 1

y \le 2x + a

x \ge 0

y \ge 0

(i) Find all real values of

a

for which the system has a feasible region. (ii) For those values of

a

, state whether the feasible region is bounded or unbounded.