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Consider the following LP problem.

Maximize $z=2x_1+3x_2,$

subject to

Constraint $1$: $4x_1+7x_{2}115,$

Constraint $2$: $3x_1+2x_{2}70,$

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 maximum value of $z?$

b$.$ Identify the binding and nonbinding constraints and

report the slack value, as applicable.