Examine whether the following system of inequalities possesses a feasible region:
(1) x+y≤2
(2) x+y≥5
(3) x≥0
(4) y≥0
Answer the sub-questions that follow.
a. (i) Draw the boundary lines corresponding to each inequality and indicate the correct half-plane for every inequality.
b. (ii) Identify the common overlapping region, if any, which satisfies all four inequalities.
c. (iii) State whether the system has at least one solution. Give a clear justification based on your graphical work in part (ii).