Consider the problem.

Min	2X2 18X + 2XY + Y2 16Y + 52
s.t. X + 4Y 6

(a) Find the values of X and Y that minimize the function and find the optimal solution value

OBJ_________ at (X, Y) = ___________

(b) If the right-hand side of the constraint is increased from 6 to 7, how much do you expect the objective function to change?

Based on the dual value on the constraint X + 4Y 6, we expect the optimal objective function value to decrease by _________ .

(c) Resolve the problem with a new right-hand side of the constraint of 7. How does the actual change compare with your estimate?

If we resolve the problem with a new right-hand-side of 7 the new optimal objective function value is -__________ , so the actual change is a decrease of ______________ rather than what we expected in part (b).

Please show work clearly and answer where the underscores are, thanks:)