Consider the following LP problem.

$1\mathrm{.}25$

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Minimize $,z=9\mathrm{.}00x_1+6\mathrm{.}20x_2,$

Subject to

Constraint $1$: $,5x_1+3x_{2}30,$

Constraint $2$: $2x_1+5x_{2}33,$

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

where $x_1$ and $x_2$ represent the decision variables. Solve the LP problem to 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 $z?$

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

$\backslash$table$[[$Value of $x_1$ at the optimal solution,$2\mathrm{.}68],[$Value of $x_2$ at the optimal solution,$5\mathrm{.}53],[$Minimum value of $z,56\mathrm{.}34]]$

b$.$ Identify the binding and nonbinding constraints and report the surplus value, as applicable. Note: If the answer to constraints is "Non$-$Binding" enter surplus value or leave cells blank.

$\backslash$table$[[$Constraint $1,,,],[$Constraint $2,,,]]$