Solve the LP by Excel Solver and then answer the following questions based on the Sensitivity Report of the original LP. You are not allowed to re-solve the LP for each of the questions.

For each of the following problems, answer the question as specifically and completely as is possible based on only the sensitivity report above, without re-solving the problem with the Solver. Type your answers directly into the spreadsheet tab labeled 3.

Note: All problems are independent (i.e., any change made in one problem part does not apply for the other problems). For full credit, you must justify your answers by utilizing the results in the sensitivity report instead of re-solving the problem with Solver.

a. If the profit on product 3 were changed to $35 a unit, what would the values of the decision variables be? The objective function? Explain.

b. If the profit on product 2 were changed to $12 a unit, what would the values of the decision variables be? The objective function? Explain.

c. If the manager decided to lay off some workers and, as a result, there were 60 fewer labor hours available, whether the optimal solution would change? Whether the optimal total profit would increase? Explain.

d. If 5 more pounds of materials were available, how much would the value of the objective function change? Whether the optimal production quantities would change? Explain.

e. If the machine needed maintenance and there were 12 fewer machine hours available, would the shadow price remain the same? Would this change the optimal values of x₁, x₂, and x₃? Explain.

MaxZ=12x1+18x2+15x3 where x1 is the quantity of product 1 to make, etc. Subject to MachineLaborMaterialsProduct2Non-negativity5x1+4x2+3x3160hours4x1+10x2+4x3288hours2x1+2x2+4x3200poundsx216unitsx10,x20,x30