Part e

Problem 3. In a product-mix-problem, X1, X2, X3, and X4 indicate the units of products 1, 2, 3, and 4, respectively, and the linear programming model is MAX Z = $5X1+$7X2+$8X3+$6X4 S.T. 1) 3X1+2x2+4x3+3X45600 Machine A hours 2) 4X1+1X2+2X3+6X45700 Machine B hours 3) 2X1+3X2+1X3+2X45800 Machine C hours Input the data in an Excel file and save the file. Using Solver, solve the problem and obtain sensitivity results. Based on the results of the sensitivity analysis answer the following questions and fully explain your answers. a. Which constraints are binding and what does it mean? Which machines have excess capacity available? How much? b. If the objective function coefficient of X1 is increased by $2, will the optimal solution change? What would be the new value of the objective function? c. Suppose the objective function coefficient of X1 is increased by 0.75, the objective function coefficient of X2 is decreased by 1.2, and the objective function coefficient of X4 is increased by 0.3. what will be the new optimal solution and the value of the objective function? Explain and support your answer. d. What should the contribution of product 4 be so it becomes profitable to produce it? Explain. e. Five hundred additional hours for Machine A can be obtained at 1.60 above the current cost. Should the additional hours be obtained at the quoted cost? Why or why not? Fully explain. If the 500 additional hours of Machine A are obtained, what will be the net increase in profits