Topics: Profit maximization, English-language films, Constraint satisfaction Pages: 4 (818 words) Published: April 21, 2013

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:

Printer| Variable| Profit| Line 1 Assembly (mins)| Line 2 Packaging (mins)| mins available per day| D1-910 | "X91"| \$42 | 3| 4| 480|
D1-950| "X95"| \$87 | 6| 2| 480|

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 recommendation?

To maximize profit with the time constraints on each line, management should only produce D1-950 printers as this model has the higher profit contribution. This strategy would involve creating 80 D1-950 printers for a total profit of \$6,960. However, implementing this strategy would create 320 minutes of dead time on line 2, leading to unutilized equipment and loitering employees.

Decision Variables| | | | |
| D1-910 | X91| 0| |
| D1-950 | X95| 80| |
| | | | |
Objective Function| | | | |
| max| (42*x91)+(87*x95)| 6960| |
| | | | |
Constraints| | | | |
Line 1 Time| 3*x91+6*x95| <=| 480| 480|
Line 2 Time| 4*x91+2*x95| <=| 480| 160|

2. Suppose that management also states that the number of DI-91O 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?

With the added constraint, production of D1-950s will decrease from 80 to 53, while D1-910s will increase from 0 to 54. The actual solver created a non-viable decimal solution, but to meet reality and constraints, the solver solution had to be adjusted...