Consider the information provided in the table below: Jobs 1 2 3 45 67 Pi 4 3 4 6 14 5 3 15 24 dj 9 35 23 33 34 a. Find the single machine job sequence that minimizes Tmax as a primary metric and F as a secondary metric. Evaluate the resulting sequence in terms of each objective function (i.e., state how much is Tmax and F for the problem. b. Add 6 time units to each due date and determine the single machine job sequence that minimizes T. Evaluate the resulting sequence in terms of T. c. Add 5 units to each due date in the original table and determine the sequence that minimizes the number of tardy jobs. d. Using the original table, find a good sequence for T. Explicitly state your strategy to find the solution. Can you guarantee optimality for your solution? Your score for this part will be based on how good your solution is compared to the optimal one. e. Use Excel's solver so find the job sequence that minimizes 3d,Cj. To use the solver go to Excel Options (under File) Add-Ins Manage (on the bottom) and select Solver Add-In. Then go to Data Solver (in the Analysis tools). When setting up your formulation, notice that there is a restriction operator called dif that forces all the values for the different decision variables to be different from each other. To be more specific, consider defining 7 decision variables (x-x-), where each represents the sequence in which the job will be performed. Notice that if they are restricted to integer values in the range of 1 to 7, and they must be different, then are modeled as permutations. We'll learn more about formulating the problems when they get more complex. For now, you should be able to create this simple model.