Consider the nonlinear optimization model stated below.

Min	2X2 18X + 2XY + Y2 16Y + 53
s.t. X + 4Y 7

(a)

Find the minimum solution to this problem.

_____ at (X, Y) = ( , )

(b)

If the right-hand side of the constraint is increased from 7 to 8, how much do you expect the objective function to change?

Based on the dual value on the constraint

X + 4Y 7,

we expect the optimal objective function value to decrease by ____.

(c)

Resolve the problem with a new right-hand side of the constraint of 8. How does the actual change compare with your estimate?

If we resolve the problem with a new right-hand-side of 8 the new optimal objective function value is___ , so the actual change is a decrease of ____ rather than what we expected in part (b).