Let R be the feasible region determined by the following system of inequalities:
(1) x+2y≥6
(2) x−y≤2
(3) x≥1
(4) y≥0
Using this information, answer the questions that follow.
a. (i) Sketch the boundary lines and shade the region R satisfying all four inequalities.
b. (ii) Show that the region R is unbounded.
c. (iii) A new inequality x+y≤7 is added to the system. Determine, with full justification, whether the feasible region remains unbounded after this addition.