Consider the following NLP problem.

Maximizez$=1\mathrm{.}5$x$212$x$1$x$2+$x$22$z$=1\mathrm{.}5$x$12-2$x$1$x$2+$x$22,$Subject to$$Constraint $1$:$2$x$1+$ x$214,$Constraint $2$:x$1,$ x$20,$

where x$1$ and x$2$ represent the decision variables. Solve this NLP problem and answer the following questions.

What are the values of x$1$ and x$2$ at the optimal solution? What is the maximum value of z$?$

Note: Round your answers to $2$ decimal places.

If the first constraint changes to $2$x$1+1\mathrm{.}1$x$214,$ what are the values of x$1$ and x$2$ at the optimal solution? What is the maximum value of z$?$

Note: Round your answers to $2$ decimal places.

If the first constraint changes to $2$x$1+$ x$212,$ what are the values of x$1$ and x$2$ at the optimal solution? What is the maximum value of z$?$

Note: Round your answers to $2$ decimal places.