A farmer plans to grow wheat on x acres and barley on y acres of his land. The agricultural guidelines impose the following conditions:
x≥2,y≥1,x+y≥5,3x+y≤20.
(i) Represent each inequality graphically, indicating the correct half–plane in every case.
(ii) Identify the feasible region that satisfies all four inequalities together.
(iii) Is the feasible region obtained in part (ii) bounded, unbounded or empty? Give a convincing explanation.
(iv) If the additional condition x+2y≤8 is also imposed, how does the classification of the feasible region change? State the new classification with justification.