Consider the nonlinear optimization model stated below.

Min $2x^2-18x+2xY+Y^2-14Y+53$

$s.t.x+4Y9$

$($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 $x+4Y9,$ we expect the optimal objective function value to decrease b$)$

$($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

expected in part $($b$).$

$,$ so the actual change is a decrease of

rather than what we