Consider the following LP problem.Constraint $1$: $5$x$1+3$x$2\backslash$geq $30,$Constraint $3$: xwhere 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.

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.

Constraint $1$

Constraint $2$

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

Note: If the answer to constraints is "Binding" enter "Shadow price" and "Range of feasibility" to $2$ decimal places or leave cells

blank.