Scenario 1
Suppose California Baptist University (CBU) is considering creating a brand new major, Medical Science, in
- If CBU sticks with its current curriculum and creates no further majors, then the annual revenue will be
tuition ($11.5 million), donation ($4.4 million), and research grants ($2.5 million). At the same time, CBU incurs
costs such as employee salaries ($6 million), rent ($5 million), and utilities ($2.2 million) to maintain its
business annually. If CBU decides to create new majors, then there are three possibilities. First, if medical
research proves to be successful, and new faculty members in medical science, receive funding more actively
from the state and federal government, then annual research grants are expected to increase from $2.5 to $8
million. Also, medical research alumni are likely to donate funds to CBU in the future, which also is expected to
increase the amount of donation from $4.4 to $6 million, so the total revenue would increase by $7.1 million.
On the other hands, the university should hire more staff/faculties in those areas, which would increase
employee salaries from $6 to $8 million, while rent and utilities stay the same as under “offering no new major”
option. However, business analysts expect this probability to be 35%. Second, there is also a 40% chance that
faculties in medical science have a hard time receiving federal research funds due to the recession, in which
case, the research grants decreases from $2.5 to $0.7 million, while revenues from tuition and donation stay
the same as under “offering no new major” option. In this scenario, CBU will still have to pay employment
salary ($8 million) and rent and utilities stay the same as under “offering no new major” option. Finally,
uncertain economic or regional factors may lead to a huge drop in enrollment, decreasing tuition revenue. The
boom in the housing market and recent drought increases rent and utilities dramatically. In other words, there is
a 25% chance that CBU is suffering a loss of $3.5 million (net profits), if it chooses to offer a new major.
Question: Make a recommendation regarding whether CBU should offer a new major or stick to its current
curriculum, using a decision tree (Hint: You MUST calculate the expected net profit of the option “offering a new
major” and compare it to the net profit of the option of “offering no new major”)
Please refer to the attached document #1 Guideline.ppsm for scenario 1.
Scenario 2
California Pacific is a lumber company that has three sources of wood and five markets to be supplied. The
annual availability of wood at sources 1, 2, and 3 is 15, 20, and 15 million board feet, respectively. The amount
that can be sold annually at markets 1, 2, 3, and 4 and 5 is 11, 12, 9, 10 and 8 million board feet, respectively.
In the past, the company has shipped the wood by train. However, because shipping costs have been
increasing, the alternative of using ships to make some of the deliveries is being investigated. This alternative
would require the company to invest in some ships. Except for these investment costs, the shipping costs in
thousands of dollars per million board feet by rail and by water (when feasible) would be the following for each
route.
Unit Cost by Rail ($1,000s) to market
Unit Cost by Ships ($1,000s) to market
Source
1
2
3
4
5
1
2
3
4
5
1
2
3
61
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69
59
72
78
66
45
60
63
55
49
61
66
56
47
31
36
38
43
33
24
28
36
24
32
35
31
26
The capital investment (in thousands of dollars) in ships required for each million board feet to be transported
annually by ship along each route is given next.
Unit Investment for Ships ($1,000s) to Market
Source
1
2
3
4
5
1
2
3
275
293
303
318
283
238
270
275
250
268
285
265
240
Considering the expected useful life of the ships and the time value of money, the equivalent uniform annual
cost of these investments is one-tenth the amount given in the table. The objective is to determine the overall
shipping plan that minimizes the total equivalent uniform annual cost (including shipping costs).
You are the head of the management science team that has been assigned the task of determining this
shipping plan for each of the three options listed next.
Option 1: Continue shipping exclusively by rail
Option 2: Switch to shipping exclusively by water (except where only rail is feasible)
Present your results for each option and compare.
Scenario 3
The vintage restaurant, on Captiva I sland near Fort M yers, Florida, is owned and operated by Karen Payne.
The restaurant just completed its third year of operation. D uring that time, Karen sought to establish a
reputation for the restaurant as a high-quality dining establishment that specializes in fresh seafood. Through
the efforts of Karen and her staff, her restaurant has become one of the best and fastest-growing restaurants
on the island. To better plan for future growth of the restaurant, Karen needs to develop a system that will
enable her to forecast food and beverage sales by month for up to one year in advance. Table 1 shows the
value of food and beverage sales ($1000s) for the first three years of operation
Table 1- Food and Beverage Sales for the Vintage Restaurant ($1,000s)
Month
Year 1
Year 2
Year 3
January
February
March
April
May
June
July
August
September
October
November
December
242
235
232
178
184
140
145
152
110
130
152
206
263
238
247
193
193
149
157
161
122
130
167
230
282
255
265
205
210
160
166
174
126
148
173
235
Perform an analysis of the sales data for the vintage restaurant. Prepare a report for Karen that summarizes
your findings, forecasts, and recommendations , i ncluding the following:
Construct a time series plot.
Comment on the underlying pattern in the time series.
Using the quarterly dummy variable approach, forecast sales for January through December of the fourth year.
For instance, you would have three dummy variables – quarter 1, quarter 2, and quarter 3 and quarter 4 is a
baseline quarter. Quarter 1=1 if sales occurs in January, February, or March, otherwise, Quarter 1=0. Quarter
2=1 if sales occurs in April, May or June, otherwise, Quarter 2=0. Quarter 3=1 if sales occurs in July, August, or
September, otherwise, Quarter 3=0.
Assume that January sales for the fourth year turn out to be $295,000. What was your forecast error? If this
error is large, Karen may be puzzled about the difference between your forecast and the actual sales value.
What can you do to resolve her uncertainty in the forecasting procedure?
Scenario 4
Better Fitness, Inc. (BFI), manufactures exercise equipment at its plant in Freeport, Long Island. It recently
designed two universal weight machines for the home exercise market. Both machines use BFI-patented
technology that provides the user with an extremely wide range of motion capability for each type of exercise
performed. Until now, such capabilities have been available only on expensive weight machines used primarily
by physical therapists. At a recent trade show, demonstrations of the machines resulted in significant dealer
interest. In fact, the number of orders that BFI received at the trade show far exceeded its manufacturing
capabilities for the current production period. As a result, management decided to begin production of the two
machines. The two machines, which BFI named the BodyPlus 100 and the BodyPlus 200, require different
amounts of resources to produce.
The BodyPlus 100 consists of a frame unit, a press station, and a pec-dec station. Each frame produced uses
4 hours of machining and welding time and 2 hours of painting and finishing time. Each press station requires 2
hours of machining and welding time and 1 hour of painting and finishing time, and each pec-dec station uses
2 hours of machining and welding time and 2 hours of painting and finishing time. In addition, 2 hours are spent
assembling, testing, and packaging each BodyPlus 100.
The BodyPlus 200 consists of a frame unit, a press station, a pec-dec station, and a leg- press station. Each
frame produced uses 5 hours of machining and welding time and 4 hours of painting and finishing time. Each
press station requires 3 hours of machining and welding time and 2 hours of painting and finishing time, each
pec-dec station uses 2 hours of machining and welding time and 2 hours of painting and finishing time, and
each leg-press station requires 2 hours of machining and welding time and 2 hours of painting and finishing
time. In addition, 2 hours are spent assembling, testing, and packaging each BodyPlus 200 .
For the next production period, management estimates that 5 00 hours of machining and welding time; 3 50
hours of painting and finishing time; and 1 2 0 hours of assembly, testing, and packaging time will be available.
The net retail price of the BodyPlus 100 and the BodyPlus 200 are $350 and $445 , respectively. A lthough
some flexibility may be available to BFI because of the unique capabilities of the new machines. Authorized
BFI dealers can purchase machines for 70% of the suggested retail price. BFI’s president believes that the
unique capabilities of the BodyPlus 200 can help position BFI as one of the leaders in high-end exercise
equipment. Consequently, she states that the number of units of the BodyPlus 200 produced must be at least 3
5% of the total production of BodyPlus 100.
Analyze the production problem at Better Fitness, Inc., and prepare a report for BFI’s president presenting your
findings and recommendations. The report should include the following items:
The recommended number of BodyPlus 100 and BodyPlus 200 machines (In other words, find the optimal
level of production for BodyPlus 100 and BodyPlus 200 using linear programming model).
Objective function: Total profit
BodyPlus 200 requirement constraint
Non-negativity constraint
Time Constraint:
Machining & Welding
Painting & Finishing
Assembly, Test, and Packaging
The effect on profits of the requirement that the number of units of the BodyPlus 200 produced must be at least
35% of the total production of BodyPlus 100. where efforts should be expended in order to increase
contribution to profits
Include a copy of your linear programming model
Levels of Achievement
Criteria
Exemplary
Accomplished
Developing
Beginning
Dimension 1: Model Specification
CLO – 1.1, 2.1