QUANTITATIVE ANALYSIS

1. OPERATION RESEARCH
AND
PRODUCTION MANAGEMENT
(TEM 706)
SUBMITTED BY: IRELYN I. JASMIN

2. Case Study Analysis
Food and Beverages at Southwestern
University Football Games

3. Based on the percentages stated in the table, these fixed costs will
be proportionately assigned to each of the items. Soft drink income, for
example, is intended to pay 25% of total fixed costs. Southwestern
University (SWU) is a significant public institution in Stephenville, Texas,
30 miles southwest of the Dallas/Fort Worth Metroplex, with about
20,000 students. SWU is a long-time football powerhouse that competes
in the Big Eleven conference and is consistently ranked in the top 20 in
college football polls. Prior to Dillon's arrival, the average attendance was
25,000–29,000. Despite the fact that the top spot remained out of reach,
attendance at the six Saturday home games climbed year after year.
1. Read and analyze the case study below through the Quantitative
Analysis Approach.

4. He told Maddux that the break-even report for the food service
area should be available for the next meeting. As a result, he desired that
the parking lots, game programs, and food service be run as profit
centers. The school is the most powerful force in the small town, with
more students than permanent residents in the fall and spring. Just the
announcement of the new coach's arrival increased season ticket sales by
10,000. Marty Starr was concerned not just about the cost of enlarging
an old stadium vs building a new one, but also about the associated
activities. SWU engaged famed Billy Bob Dillon as its head coach in 2013
in order to improve its prospects of obtaining the elusive and long-
desired number-one rating.

5. He wanted to make sure that the various support
initiatives brought in enough money to cover their costs. Dr.
Starr, president of Southwestern University, directed Hank
Maddux, the stadium manager, to create a break-even chart
and accompanying data for each of the centers during a recent
discussion about the new stadium. More renown, the need for a
larger stadium, and more concerns about seats, parking, long
lines, and concession stand costs came with the increase in
attendance.

6. 2. Utilize the following:
a. Schematic Model (concept map);
and
b. Mathematical Model

7. a. Schematic Model (concept map)
Formulate
mathematical
model
CASE STUDY: Food and
Beverages at
Southwestern University
Football Games MATHEMATICAL
MODEL
REAL PROBLEM/
SITUATION
Select
Appropriate
math tools
Solve
mathematical
problem
Determine and
Estimate
parameters
Validate
solution
Visualize
solution
Draw
appropriate
conclusions
Communicate
result
Making
simplifying
assumptions
Identifying
governing
principles
Identify
variables and
principles
Define question
interest

8. b. Mathematical Model
MATHEMATICAL
MODEL
THEORY
NUMERICAL
METHODS
PROBLEM
STATEMENT
REPORT
PROGRAMS

9. Case Study 1. Prepare a brief report with the items noted so it
is ready for Dr.Starr at the next meeting.
Item Selling Variable Percent
Price/Unit
Cost/Unit Revenue
Soft drink 1.50 0.75 25%
Coffee 2 0.5 25%
Hot Dogs 2 0.8 20%
Hamburgers 2.5 1 20%
Misc. snacks 1 0.4 10%

10. The total fixed cost per game includes salaries, cost of workers
in six booths and rental fees.
SOUTHWESTERN UNIVERSITY
Data
• Salaries $20,000.00
• Rental fees 2,400 x $2= $4,800
• Booth worker wages 6 x 6 x 5 x $7 = $1,260
• Total fixed cost $20,000 + $4,800 + $1,260 = $26,060

11. The cost of this allocated to each food
item is shown in the table:
Percent Allocated fixed
Item revenue cost
Soft drink 25% $6,515
Coffee 25% $6,515
Hot dogs 20% $5,212
Hamburgers 20% $5,212
Misc. snacks 10% $2,606

12. The break-even points for each of these items are found by computing the contribution
to profit (profit margin) for each item and dividing this into the allocated fixed cost.
These are shown in the next table:
Item
Selling
price
Variable Profit
cost margin
Percent
revenue
Allocated
fixed cost
Break even
volume
Soft drink $1.50 $0.75 $0.75 25% 6515 8686.67
Coffee $2.00 $0.50 $1.50 25% 6515 4343.33
Hot dogs $2.00 $0.80 $1.20 20% 5212 4343.33
Hamburgers $2.50 $1.00 $1.50 20% 5212 3474.67
Misc. snacks $1.00 $0.40 $0.60 10% 2606 4343.33
÷

13. Selling Break even
Dollar
volume
Item price volume of sales
Soft drink $1.50 8686.67 $13,030.00
Coffee $2.00 4343.33 $8,686.67
Hot dogs $2.00 4343.33 $8,686.67
Hamburgers $2.50 3474.67 $8,686.67
Misc. snacks $1.00 4343.33 $4,343.33
Total $43,433.34
To determine the total sales for each item that is required to break even,
multiply the selling price by the break even volume. The results are shown:

14. Thus, total sales must be $43,433.34 to break even. If
there are 35,000 individuals in attendance, each person
must spend $43,433.34/35,000 = $1.24. If there are
60,000 people in attendance, each person will have to
spend $43,433.34/60,000 = $0.72. Given that both of
these figures are extremely low, we can be confident that
this food and beverage establishment will at the very
least break even.