Two responses y₁ and y₂ are related to two inputs x₁ and x₂ by the models y₁ = 5 (x₁ – 2)² + (x₂ − 2)³ and y₂ = x₂ – x₁ + 3. Suppose that the objectives are y₁ ≤ 9 and y₂ ≥ 6.

(a) Is there a feasible set of operating conditions for x₁ and x₂? If so, plot the feasible region in the space of x₁ and x₂.

(b) Determine the point(s) (x₁, x₂ ) that yields y₂ ≥ 6 and minimizes y₁.