Consider the nonlinear optimization model stated below.

Min	2X218X+ 2XY+Y212Y+51
s.t. X+ 4Y7

(a)Find the minimum solution to this problem.

______at (X,Y) = ( , )

(b)If the right-hand side of the constraint is increased from7to8, how much do you expect the objective function to change?Based on the dual value on the constraint

X+ 4Y7,

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

(c)Resolve the problem with a new right-hand side of the constraint of8. How does the actual change compare with your estimate?

- If we resolve the problem with a new right-hand-side of8the new optimal objective function value is _______________ ,so the actual change is a decrease of ___________ rather than what we expected in part (b).