Consider the nonlinear optimization model stated below.

Min $2x^2-18x+2xY+Y^2-12Y+53$

$s.t.x+4Y8$

$($a$)$ Find the minimum solution to this problem.

$xat(x,Y)=(,)$

$($b$)$ If the right$-$hand side of the constraint is increased from $8$ to $9,$ how much do you expect the objective function to change?

Based on the dual value on the constraint $x+4Y8,$ we expect the optimal objective function value to decrease by

$($c$)$ Resolve the problem with a new right$-$hand side of the constraint of $9.$ How does the actual change compare with your estimate?

If we resolve the problem with a new right$-$hand$-$side of $9$ the new optimal objective function value is

expected in part $($b$).$