Consider the nonlinear optimization model stated below.

Min$2$X$218$X $+2$XY $+$ Y$212$Y $+51$

s$.$t$.$ X $+4$Y $6$

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

$\_\_\_\_$ at $($X$,$ Y$)=(4\mathrm{.}08,0\mathrm{.}48)$

$($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 $8\mathrm{.}56,$ so the actual change is a decrease of $\_\_\_\_$ rather than what we expected in part $($b$).$