MGOC10 Fall 2025
Assignment 1. Worth: 10%. Due: October 17, 2025, by the end of the day
(11:59 pm). Please submit via Quercus under ASSIGNMENTS. This assignment
is individual, every student should submit their own work.
You should write managerial reports for the following two problems:
Problem 1. A firm makes three components for sale to refrigeration companies. Each
component must be processed on two machines: a shaper and a grinder. The times (in
minutes) per unit required on each machine are as follows:
Component
1
2
3
Shaper
6
4
4
Grinder
4
5
2
The shaper is available for 120 hours, and the grinder is available for 110 hours. No more
than 200 units of component 3 can be sold, but up to 1000 units of each of the other two
components can be sold. In fact, the company already has orders for 600 units of
component 1 that must be satisfied. The profit contributions for components 1, 2, and 3
are $8, $6, and $9, respectively.
a) Formulate a linear programming model to maximize profit and solve for the
recommended production quantities.
b) What are the objective coefficient ranges for the three components? Interpret
these ranges for company management.
c) What are the right-hand-side ranges? Interpret these ranges for company
management.
d) If more time could be made available on the grinder, how much would it be
worth?
e) If more units of component 3 can be sold by reducing its sales price by $4, should
the firm reduce the price?
Problem 2. A company manufactures kitchen cabinets. Because of a large backlog of
orders for oak and cherry cabinets, the company decided to contract with three smaller
cabinetmakers to do the final finishing operation. For the three cabinetmakers, the
number of hours required to complete all the oak cabinets, the number of hours required
to complete all the cherry cabinets, the number of hours available for this final finishing
operation, and the cost per hour to perform the work are shown here.
Cabinetmaker 1 Cabinetmaker 2
Hours required to complete 50
42
all the oak cabinets
Hours required to complete 60
48
all the cherry cabinets
Hours available
40
30
Cost per hour
$36
$42
Cabinetmaker 3
30
35
35
$55
For example, Cabinetmaker 1 estimates it will take 50 hours to complete all the oak cabinets and
60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours
available. Thus, Cabinetmaker 1 can only complete 40/50=0.80, or 80%, of the oak cabinets if it
worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 40/60=0.67, or 67%,
of the cherry cabinets if it worked only on cherry cabinets.
a. Formulate a linear programming model that can be used to determine the percentage of
the oak cabinets and the percentage of the cherry cabinets that should be given to each of
the three cabinetmakers in order to minimize the total cost of completing both projects.
b. Solve the model formulated in part (a). What percentage of the oak cabinets and what
percentage of the cherry cabinets should be assigned to each cabinetmaker? What is the
total cost of completing both projects?
c. If Cabinetmaker 1 has additional hours available, would the optimal solution change?
Explain.
d. If Cabinetmaker 2 has additional hours available, would the optimal solution change?
Explain.
e. Suppose Cabinetmaker 2 reduced its cost to $38 per hour. What effect would this change
have on the optimal solution? Explain.
The problems should be addressed in your assignment in this order. Please clearly separate the
problems, starting the second problem on a new page. Each page should have a header indicating
which problem this page corresponds to. The assignment is individual. On the front page, put
your name, student number, course (MGOC10 “Analytics for Decision Making”), term (Fall
2025), professor’s name (Igor Averbakh), and list your section (e.g., L01, L02, L03, L04).
Your managerial report for each problem should have the following structure:
1) Executive summary (approximately one-third to one-half of a page for each problem, any
font any spacing, but should look nice);
2) Detailed report.
The executive summary for each problem should include a brief verbal description of the
situation in your words (without numerical data) and a summary of your work and conclusions
(the summary can include numerical results). Place the executive summary at the beginning of
your report for the problem, under the heading “Executive Summary”. The executive summary is
the summary of your MAIN findings: this is what your boss would read first, and if (s)he doesn’t
like it, (s)he may not want to read the rest. So, it must be very clear, well-written and polished.
The detailed report should include all details of the model (clearly define your decision
variables!), then answer the questions posed in the problem. Answers to the questions should be
clearly identified (e.g., “Question b”) so that it is easy for the grader to find them. The detailed
report should make clear references to computer outputs that must be also included as
screenshots in appendices. Please include screenshots of the original Excel outputs, not
summaries, not tables that you draw yourself based on the outputs. The screenshots should
support your answers. Answers without the supporting screenshots of computer outputs may not
be credited. Do not put the screenshots in the main body of the report, only in appendices. The
appendices should be placed at the end of the assignment, after the reports for both problems, and
should be clearly identified.
As for computer outputs for the models, please include (1) the spreadsheet, (2) the Solver
Parameters screen.
Your assignments must be typed. Handwritten assignments will not be accepted. Quality of
presentation is a significant component in evaluation. The assignment will be graded based on
correctness, logic, completeness, clarity and quality of presentation, grammatical and stylistic
correctness, and overall impression (yes, in real life reports not only have to be correct, but also
should make good impression!) Note that evaluation of presentation is based on the subjective
impression of the grader; clarity and ease of finding all necessary information is an important
component.
You should use the Excel solver for this assignment. Detailed explanations on how to use the
solver are available in the book. Examples on using Excel solver are available in each of the
Chapters 2-4. Also, you can see the posted Topic 3 on Quercus. You should carefully work out
these examples to understand how to use the solver. Appendix A in the book has some basic
material on spreadsheet models.
To ensure that all students have equal chances, to make the setting closer to a real-life project and
to introduce an element of independent learning to the course, the general policy with respect to
the assignments is that neither the professor nor the T.A. will give you ANY help with using the
software – this you should figure out yourself. Nor will we help with any specific questions about
your problems. However, general conceptual questions about the course material are very
welcome.