Implement the following LP problem in a spreadsheet. Use Solver to solve the problem and create a Sensitivity Report. Use the information to answer the following questions:

MAX: $2$X$1+4$X$2$

Subject to:

$$X$1+2$X$2<=8$

X$1+2$X$2<=12$

X$1+$ X$2>=2$

X$1,$ X$2>=0$

a$.$ Which of the constraints are binding at the optimal solution?

b$.$ Is the optimal solution to this problem unique, or is there an alternate optimal solution?

c$.$ What is the optimal solution to this problem if the value of the objective function coefficient for variable X$1$ is zero?

d$.$ How much can the objective function coefficient for variable X$2$ decrease before changing the optimal solution?

e$.$ Given the objective in this problem, if management could increase the RHS value for any of the constraints for identical costs, which would you choose to increase and why?