$(20$ points total$)$ Consider the solution of the following linear programming problem. Use the output shown below to answer the following questions.

Midterm Sensitivity Analysis Final.JPG

Alternate Version

$(4$ points$)$ Determine the slack of constraint $1.$ Show your calculation clearly on how you determined this slack value. Is constraint $1$ a binding constraint? Why or why not?

$(3$ points$)$ Notice that the current value of X$2$ in the optimal solution is $0.$ If the coefficient of X$2$ in the objective function is increased to $45$ and the problem is re$-$solved, will the value of X$2$ at optimality be impacted? Why or why not?

$(8$ points$)$ If the objective function coefficient of all variables simultaneously increase by $5$ units each, would the current solution still remain optimal? Will the objective function value be impacted at all? Explain your answer.

$(5$ points$)$ All else remaining the same, what action would you recommend so that X$2$ becomes positive at optimality? Explain your answer.