Consider the following NLP problem.

Minimize $,z=1-2e^{-(5x_1^2+2x_2^2)},$

subject to

Constraint $1$: $2x_1+1\mathrm{.}1x_{2}2,$

Constraint $2$ : $x_1,x_{2}0,$

Constraint $3$:$x_1,x_{2}1,$

where $x_1$ and $x_2$ represent the decision variables. Solve this NLP problem and answer the

following questions.

a$.$ What are the values of $x_1$ and $x_2$ at the optimal solution? What is the minimum value of $z?$

b$.$ If the first constraint changes to $2x_1+1\mathrm{.}1x_{2}2\mathrm{.}5,$ what are the values of $x_1$ and $x_2$ at the

optimal solution? What is the minimum value of $z?$