Digital Imaging (DI) produces photo printers for both the professional and consumer markets. The DI consumer divisionrecently introduced two photo printers that provide color printsrivaling those produced by a professional processing lab. TheDI-910 model can produce a 4 x 6 inch borderless print inapproximately 37 seconds. The more sophisticate and fasterDI-950 can even produce a 13 x 19 inch borderlessprint. Financial projections show profit contributions of $42for each DI-910 and $87 for each DI-950. The printers are assembled, tested, and packaged atDI’s plant located in New Bern, North Carolina. Thisplant is highly automated and uses two manufacturing lines toproduce the printers. Line 1 performs the assembly operationwith times of 3 minutes per DI-910 printer and 6 minutes per DI-950printer. Line 2 performs both the testing and packagingoperations. Times are 4 minutes per DI-910 printer and 2minutes per DI-950 printer. The shorter time for the DI-950printer is a result of its faster print speed. Bothmanufacturing lines are in operation one 8-hour shift perday.
Define Constrtaints and objective function
1. The recommended number of units of each printer to produce tomaximize the total contribution to profit for an 8-hourshift. What reasons might management have for not implementingyour recommendation? 2. Suppose that management also states that the number of DI910printer produced must best at least as great as the number ofDI-950 units produced. Assuming that theobjective is to maximize the total contribution to profit for an8-hour shift, how many units of each printer should beproduced? 3. Does the solution you developed in part (2) balance the totaltime spent on line 1 and the total time spent on line2? Whymight this balance or lack of it be a concern tomanagement? 4. Management requested an expansion of the model in part (2)that would provide a better balance between the total time on line1 and the total time on line 2. Management wants to limit thedifference between the total time on line 1 and the total time online 2 to 30 minutes or less. If the objective is still tomaximize the total contribution to profit, how many units of eachprinter should be produced? What effect does this workloadbalancing have on total profit in part (2)? 5. Suppose that in part (1) management specified the objectiveof maximizing the total number of printers produced each shiftrather that total profit contribution. With this objective,how many units of each printer should be produced pershift? What effect does this objective have on total profitand workload balancing?