Instructions: Solve the following problems by writing your full solutions and final answers on regular sized bond papers. Write your solutions manually.

CASE:

Digital Imaging (DI) produces photo printers for both professional and consumer markets. The DI consumer division recently introduced two photo printers that provide color prints rivalling those produced by a professional processing lab. The DI-910 model can produce a 4”X6” borderless print in approximately 37 seconds. The more sophisticated and faster DI-950 can even produce a 13”x19” borderless print. Financial projections show profit contributions of $42 for each DI-910 and $87 for each DI-950.

The printers are assembled, tested and packaged at DI’s plant located in New Bern, North California. This plant is highly automated and uses two manufacturing lines to produce the printers. Line 1 performs the assembly operations with times of 3 minutes per DI-910 printers and 6 minutes per DI-950 printer. Line 2 performs both the testing and packaging operations. Times are 4 minutes per DI-910 and 2 minutes per DI-950. The shorter time for DI-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 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.

1. The recommended number of units of each printer to produce to maximize the total contribution to profit for an 8-hour shift. What reasons might management have for not implementing your recommendations?

2. Suppose that the management also states that the number of DI-910 printers produced must be at least as great as the number of DI-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?

3. Does the solution in (2) 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 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 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 (2)?

5. Suppose that in (1) management specified the objective of maximizing the total number of printers produced each shift rather than the 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 balancing?

NOTE: FOR EACH SOLUTION THAT YOU DEVELOP INCLUDE A COPY OF YOUR LINEAR PROGRAMMING MODEL.