construct several versions of a linear optimization model and prepare a brief managerial
report that communicates your findings for each. Your submission should be structured as follows:
1. A brief summary of the business problem.
2. Answers to each of the numbered questions. This information should be communicated in well-written
paragraphs. Answers that are simply numbers and/or fragmented sentences will not receive full credit.
3. An appendix containing the R code used to generate the optimization model. Your code should be clean and
commented.
Note that you do not need to solve these questions using the graphical method: it is sufficient to complete this work in R.
Case Study: Pixel Perfect Imaging
Pixel Perfect Imaging (PPI) is a company that manufactures high-quality commercial printers. The research and
development team in PPI’s engineering division has recently completed the design on two new models: the PPI-100 and
the PPI-200. The PPI-100 model is intended for medium-sized vinyl banners and posters and can produce a full color print
up to 3’ wide and 8’ long in about 15 minutes. The PPI-200 model is intended for heavier use: this model can produce
prints up to 5’ wide and 12’ long in an even shorter amount of time (about 10 minutes.) Financial projections indicate that
each PPI-100 sold will have a profit contribution of $336, while each PPI-200 sold will have a profit contribution of $696.
Production of both models occurs at PPI’s manufacturing plant in Akron, Ohio. The production process is mostly
automated and split between two lines: Line 1 handles the assembly of each unit. Each PPI-100 requires 6 minutes to
assemble, while each PPI-200 requires 12 minutes to assemble. Line 2 handles both the quality assurance testing and
packaging for each unit, a process which takes 8 minutes per PPI-100 and 4 minutes per PPI-200 (the PPI-200 is able to
be tested more quickly because it has a faster print speed.) Lines 1 and 2 both operate for a single 9-hour shift each day.
1. Construct a linear optimization model to determine the optimal number of units of each model that should be
produced during each shift in order to maximize the daily total profit contribution. Briefly summarize your
recommendation, including any potential issues this course of action might pose.
2. Create a second iteration of your model that changes the objective from maximizing profit contribution to
maximizing the total number of printers produced in each shift. Briefly summarize your recommendation, including
an estimate of the daily total profit contribution achieved using this strategy.
3. Return to your original objective of maximizing total daily profit contribution. The COO of Pixel Perfect is
advocating that in each shift, the number of PI-100 units produced should be at least equal to the number of PI200 units produced. Create an alternate version of your model from part (1) that reflects the COO’s requirement
and briefly summarize your recommendation.
4. The senior management team would also like a version of your original model that attempts to balance the
lengths of time each manufacturing line spends in operation each day. Create an alternate version of your model
from part (1) that limits the difference between each line’s total operating time to no more than half an hour. Note
that this model does not need to incorporate the constraint introduced in part (3).