Consider the nonlinear optimization model stated below.

Min $2x^2-18x+2xY+Y^2-14Y+56$

$s.t.x+4Y9$

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

$at(x,Y)=(,)$

$(b)If$ the right$-$hand side $of$ the constraint $is$ increased from $9to10,$ 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 $by$

$(c)$ Resolve the problem with a new right$-$hand side $of$ the constraint $of10.$ How does the actual change compare with your estimate?

$Ifwe$ resolve the problem with a new right$-$hand$-$side $of10$ the new optimal objective function value $is$

$,so$ the actual change $is$ a decrease $of$

rather than what $we$ expected $in$ part $(b).$ Consider the nonlinear optimization model stated below.

Min $2x^2-18x+2xY+Y^2-14Y+56$

$s.t.x+4Y9$

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

$at(x,Y)=(,)$

$(b)If$ the right$-$hand side $of$ the constraint $is$ increased from $9to10,$ 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 $by$

$(c)$ Resolve the problem with a new right$-$hand side $of$ the constraint $of10.$ How does the actual change compare with your estimate?

$Ifwe$ resolve the problem with a new right$-$hand$-$side $of10$ the new optimal objective function value $is$

$,so$ the actual change $is$ a decrease $of$

rather than what $we$ expected $in$ part $(b).$