Consider the nonlinear optimization model stated below. Min 2X2 18X + 2XY + Y2 16Y + 54 s.t. X + 4Y 9

(a) Find the minimum solution to this problem. at (X, Y) = (b) If the right-hand side of the constraint is increased from 9 to 10, how much do you expect the objective function to change? Based on the dual value on the constraint X + 4Y 9, we expect the optimal objective function value to decrease by .

(c) Resolve the problem with a new right-hand side of the constraint of 10. How does the actual change compare with your estimate? If we resolve the problem with a new right-hand-side of 10 the new optimal objective function value is , so the actual change is a decrease of rather than what we expected in part (b).