Find the answer for the following casestudy through linear programming graphical method

Case Study: WORKLOAD BALANCING Digital Imaging {DI} produces photo printers for both the professional and consumer markets. The DI consumer division recently introduced two photo printers that provide color prints rivaling those produced by a professional processing lab. The DI-91ll mode] can produce a 4-" 3-! 6" borderless print in approximately 3? seconth. The more sophisticated and tater DI-95il can even produce a 13" X [9\" borderless print. Financial projections show prot contributions of $42 for each DI-'llilI and $8? for each DI-Qil. The printers are assembled, tested. and packaged at DI's plant located in New Bern. North Carolina This plant is highly automated and uses two manufacturing lines to produce the printers. Line I performs the assembly operation with times of 3 minutes per DI-Qlil printer and 6 minutes per DI-'i'SflI printer. Line 2 performs both the testing and packaging operations. Times are4 minutes per DI-ftlll printer and 2 minutes per DI-95ll printer. The shorter time for the DI-jSl printer is a result of its faster print speed. Both manufacturing lines are in operation one 3-hour shift per day. Managerial Report Perform an analysis for Digital Imaging in order to determine how many units of each printer to produce. Prepare a report to DI's president presenting your findings and recommendations. Include [but do not limit your discussion to} a consideration of the following: I. The recommended number of units of each printer to produce to maximize the total contribution to prot for an Ephour shift. What reasons might management have for not implementing your recommendation. 2. Suppose that management also states that the number of DI-DIIJ printers produced must be at least as great as the number of DI-'JSIl units producerL Assuming that the objective is to maximize the total contribution to profit for an 3-hour shift. how many units of each printer should be produced? 3. Does the solution you developed in part {2} balance the total time spent on line I and the total time spent on line 2? Why might this balance or lack of it be a concern to management? 4. Management requested an expansion of the model in part [2} that would provide a better balance between the total time on line I and the total time on line 2. Management wants to limit the difference between the total time on line I and the total time on line 2 to 3ft minutes or less. If the objective is still to maximize the total contribution to profit. how many units of each printer should be produced? What effect does this workload balancing have on total profit in part (2]? 5. Suppose that in part [1} management specified the objective of maximizing the total number of printers produced in each shift rather than total pmt conu'ibution. With this objective. how many units of each printer should be produced per shift? What effect does this objective have on total profit and workload balancing