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

MIN: 5X1 + 3X2 + 4X3

Subject to: X1 + X2 + 2X3 ≥ 2

5X1 + 3X2 + 2X3 ≥ 1

X1, X2, X3 ≥ 0

a. What is the smallest value the objective function coefficient for X3 can assume without changing the optimal solution?

b. What is the optimal objective function value if the objective function coefficient for X3 changes to –1? (The answer to this question is not given in the Sensitivity Report. Consider what the new objective function is relative to the constraints.)

c. What is the optimal objective function value if the RHS value of the first constraint increases to 7?

d. What is the optimal objective function value if the RHS value of the first constraint decreases by 1?

e. Will the current solution remain optimal if the objective function coefficients for X1 and X3 both decrease by 1?