# Linear Programming : Optimization Using Excel and a Graphical Method

Case Problem - Workload Balance

Chicago Digital Imaging produces photo printers for both the professional and consumer markets. The Chicago Digital Imaging division recently introduced two photo printers that provide color prints rivaling those produced by a professional processing lab. The Chicago Digital Imaging 910 model can produce a 4" X 6" borderless print in approximately 37 seconds. The more sophisticated and faster Chicago Digital Imaging 950 model can even produce a 13" X 19" borderless print. Financial projections show profit contributions of $42 for each Chicago Digital Imaging 910 model and $87 for each Chicago Digital Imaging 950 model.

The printers are assembled, tested, and packaged at Chicago Digital Imaging's plant located in North Carolina. This plant is highly automated and uses two manufacturing lines to produce the printers. Line 1 performs the assembly operation with times of 3 minutes per Chicago Digital Imaging 910 model and 6 minutes per Chicago Digital Imaging 950 model. Line 2 performs both the testing and packaging operations. Times are 4 minutes per Chicago Digital Imaging 910 printer and 2 minutes per Chicago Digital Imaging 950 model. The shorter time for the Chicago Digital Imaging 950 printer is a result of its faster print speed. Both manufacturing lines are in operation one 8-hour shift per day.

Perform an analysis for Chicago Digital Imaging in order to determine how many units of each printer to produce. Prepare a report to Chicago Digital Imaging regarding findings and recommendations. Include consideration of the following:

A). Recommended number of units of each printer to produce to maximize the total contribution to profit for an 8-hour shift. What reasons may management have for not implementing a recommendation?

B). Suppose management also states the number of Chicago Digital Imaging 910 printers produced must be at least as great as the number of Chicago Digital Imaging 950 units produced. Assuming that the objective is to maximize the total contribution to profit for an 8-hour shift, how many units of each printer should be produced?

C). Does the solution developed in question (B) balance the total time spent on line 1 and the total time spent on line 2? Why might this balance or lack of it be a concern to management?

D). Management requested an expansion of the model in part (B) that would provide a better balance between the total time on line 1 and the total time on line 2. Management wants to limit the difference between the total time on line 1 and the total time on line 2 to 30 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 (B)?

E).Suppose that in part (A) management specified the objective of maximizing the total number of printers produced each shift rather than total profit contribution. 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 balance?

For each solution that is developed, prepare linear programming model in Excel and graphical solution in report.

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#### Solution Summary

A LP problem is solved using a graphical method and Excel. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.