A manufacturer of cutting tools has developed two empirical equations for tool life in hours (y 1 ) and for tool cost in dollars (y 2 ) Both models are linear functions of steel hardness (x 1 ) and manufacturing time (x 2 ) The two equations are y 1 10 5x 1 2x 2 y 2 23 3x 1 4x 2 and both equations ...

To determine whether there is a feasible set of operating conditions for this process we need to che ...

A manufacturer of cutting tools has developed two empirical equations for tool life in hours (y 1

Question:

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

ŷ₁ = 10 + 5x₁ + 2x₂

ŷ₂ = 23 + 3x₁ + 4x₂

and both equations are valid over the range -1.5 ≤ x_i ≤ 1.5. Unit tool cost must be below $27.50 and life must exceed 12 hours for the product to be competitive. Is there a feasible set of operating conditions for this process? Where would you recommend that the process be run?

Fantastic news! We've Found the answer you've been seeking!