Consider the following LP problem.

Naxinize $z-2\mathrm{.}93x_1+1\mathrm{.}90x_2,$

Subject $to2x_1+3x_{2}40,$

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

Constraint $2$: $x_1,x_{2}20,$

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 maximum value of $z?$

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

$\backslash$table$[[$Value of $x_1$ at the oplimal solution,$],[$Value of $x_2$ at the oplimal solution,$],[$Maximum value of $z,]]$

b$.$ Identify the binding and nonbinding constraints ond report the slack value; as applicable.

Note: If the answer to constraints is "Non$-$Binding" enter slack value to $2$ decimal places or leave cells blank.

$\backslash$table$[[$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 the "Shadow price" and "Range of feasibility" to $2$ decimal places or leave cells blank.

$\backslash$table$[[$A$,$Shadow Price,Range of Feasibulity$],[$From$,$To$],[$Constraint $1,,,],[$Constraint $2,,,]]$

d$.$ What is the range of optimality for the two objective function coefficients?

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

$\backslash$table$[[,\backslash$table$[[$Range of Optimality for the$],[$Objective Function$],[$Coemielents$]]],[,$From,To$],[x_1,,],[x_2,,]]$

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