A manufacturer of cutting tools has developed two empirical equations for tool life (y₁) and tool cost (y₂). Both models are functions of tool hardness (x₁) and manufacturing time (x₂). The equations are

ŷ₁ = 10 + 5x₁ + 2x₂

ŷ₂ = 23 + 3x₁ + 4x₂

and both are valid over the range –1.5 ≤ x_i ≤ 1.5. Suppose that tool life must exceed 12 hours and cost must be below $27.50.

(a) Is there a feasible set of operating conditions?

(b) Where would you run this process?