Consider the following LP problem.

Minimize $,z=8\mathrm{.}90x_1+5\mathrm{.}90x_2,$

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,$0\mathrm{.}00],[$Value of $x_2$ at the optimal solution,$6\mathrm{.}60],[$Minimum value of $z,38\mathrm{.}94]]$

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 $1,$Binding,$],[$Constraint $2,$Binding,$]]$

c$.$ Report the shadow price and range of feasibility of each binding constraint.