Consider the following NLP problem.

Maximize

$z=1\mathrm{.}5x_1^2-2x_1{x}_2{x}_2^2$

Subject to

Constraint $1$: $,2x_1{x}_{2}18,$

Constraint $2$: $,3x_1,x_{2}0,$

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 maximum value of $z?$

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

Answer is complete but not entirely correct.

$\backslash$table$[[$Value of $x_1$ at the optimal solution,$5\mathrm{.}68],[$Value of $x_2$ at the optimal solution,$6\mathrm{.}63],[$Maximum value of $z,66\mathrm{.}70x$