Assignment #3: Case Problem "Julia's Food Booth" Page 1

Case Problem "Julia's Food Booth"

Jenna Kiragis

Strayer University

8/24/2012

Assignment #3: Case Problem "Julia's Food Booth" Page 2 A) Formulate and solve an L.P. model:
Variables:
x1 – Pizza Slices
x2 – Hot Dogs
x3 – Barbeque Sandwiches
Subject to:
$0.75x1 + $0.45x2 + $0.90x3 ? $1,500
24x1 + 16x2 + 25x3 ? 55,296 in2 of oven space
x1 ? x2 + x3 (changed to –x1 + x2 + x3 ? 0 for constraint) x2/x3 ? 2 (changed to –x2 +2x3 ? 0 for constraint)
x1, x2, x3 ? 0
Solution:
Variable | Status | Value |
X1 | Basic | 1250 |
X2 | Basic | 1250 |
X3 | NONBasic | 0 |
slack 1 | NONBasic | 0 |
slack 2 | Basic | 5296.0 |
slack 3 | NONBasic | 0 |
slack 4 | Basic | 1250 |
Optimal Value (Z) | | 2250 |

Assignment #3: Case Problem "Julia's Food Booth" Page 3

B) Evaluate the prospect of borrowing money before the first game.

Yes, Julia would increase her profit if she borrowed some more money from a friend. The shadow price, or dual value, is $1.50 for each additional dollar that she earns. The upper limit given in the model is $1,658.88, which means that Julia can only borrow $158.88 from her friend, giving her an additional profit of $238.32. Based on the sensitivity analysis, the upper limit of the sensitivity range for budget is $158.00 allowing her to have a maximum budget of $1658.00. Her shadow price reflects an increase of $1.50 for any additional resource. Therefore if she borrows the maximum of $158.88, she will yield an increase in profit of $238.32 and total profit of $2,488.32.

C) Prospect of paying a friend $100/game to assist

Yes, I believe Julia should hire her friend for $100 per game. In order for Julia to prepare the hot dogs and barbeque sandwiches needed in a short period of time to make her profit, she needs the additional help. Also, with...

...Assignment3: Julia Bond Booth
Julia is a senior at Tech, and a small entrepreneur. She wants to lease a food booth outside the Tech stadium for the home football games, so she can make profit to finance a final year. Tech sells out every home game, and the one thing Julia knows from attending the every games, is that everyone eats a lot of food. She has a booth, and the booths are not very large. Vendors can sell either food or drinks on Tech property, but not both. Only the Tech athletic department concession stands can sell both inside the stadium. Then, she had a great idea, she thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans and so these are the items she would sell.
(A) Formulate and solve an L.P. Model for this case.
X1= the number of slices of Pizza; X2 = the number of Hot Dogs; X3 = the number of Sandwiches
**The Objective is to Maximize Total Profit. Profit is calculated for each variable by subtracting cost from the selling price**
For Pizza Slice, Cost/Slice= $6/8 = $0.75
For Hot Dog = $1.50 – 0.45 = $1.05
For Sandwiches = $2.25 – 0.90 = $1.35
**Maximize**
Z = $0.75(x1) + $1.05(x2) + $1.35(x3)
$0.75(x1) + $0.45(x2) + $0.90(x3) = 2.1
x1,x2,x3 >= 0
**Constraints**
$0.75(x1) + $0.45(x2) + $0.90(x3) =0 (At least twice as many Hot Dogs as BBQ.)
x1, x2, x3 >0 (non-negativity constraint) |
Hot Dogs: 1250; BBQ Sandwiches: 0; Pizza: 1250
Amount of Total Food :...

...MAT540 Quantitative Analysis Quiz 3
TRUE/FALSE – clearly indicate your response.
1. Sensitivity analysis is the analysis of the effect of parameter changes on
the optimal solution. T .
2. The sensitivity range for an objective function coefficient is the range of
values over which the current optimal solution (product mix) will remain
optimal. T .
3. The sensitivity range for a right-hand-side value in a constraint is the
range of values over which the quantity values can change without
changing the solution variable mix, including slack variables. T .
4. The terms reduced cost, shadow price, and dual price all mean the same
thing. F .
5. Sensitivity analysis can be used to determine the effect on the solution
for changing several parameters at once. F .
6. A negative shadow price indicates that the objective function decreases
when the right hand side of a constraint increases. T .
7. For a profit maximization problem, if the allowable increase for a
coefficient in the objective function is infinite, then profits are unbounded. T .
MULTIPLE CHOICE – clearly indicate your response.
1. For a linear programming problem, assume that a given resource has not been fully used. In other words, the slack value associated with...

...term of form six.
MANUAL FOR COURSEWORK
The manual contains regulations and guidelines on
the conduct and assessment of coursework which
needs to be implemented by the school as well as
coursework assignments.
The school authority is responsible to make copies of
Part 2: Student’s Manual For Mathematics (T)
Coursework of this manual to be given to the
students.
Student are required to complete the coursework
which comprises three assignments in the respective
terms.
IMPLEMENTATION
Students must carry out each assignment
individually. Plagiarism will be penalised.
Teachers must monitor the progress of the
student’s coursework. It is, however, not
acceptable for teachers to give detailed
suggestions as to how the work may be improved
to meet the assessment criteria.
Examples of unacceptable assistance are as
follows:
•
detailed
omissions
indication
of
errors
or
•
the provision of detailed outlines,
analysis, discussion, or conclusion specific to the
coursework tasks
•
personal intervention to improve the
presentation or content of the coursework
ASSIGNMENT REPORTS
A complete assignment report should be structured
as follows:
(a)
Introduction
(b)
Methodology
(c)
Results
(d)
Conclusion
ASSIGNMENT REPORTS
(a) Introduction:
•Description of the problem (including the title)
(b) Methodology
•The application...

...Analytic skills
3) Management scientists use the terms "data" and "information" interchangeably--that is, the two terms mean the same thing
Answer: FALSE
Diff: 2 Page Ref: 4
Section Heading: The Management Science Approach to Problem Solving
Keywords: data
AACSB: Analytic skills
4) A management science solution can be either a recommended decision or information that helps a manager make a decision
Answer: TRUE
Diff: 2 Page Ref: 5
Section Heading: The Management Science Approach to Problem Solving
Keywords: model, management science techniques
AACSB: Analytic skills
5) A variable is a value that is usually a coefficient of a parameter in an equation.
Answer: FALSE
Diff: 1 Page Ref: 3
Section Heading: The Management Science Approach to Problem Solving
Keywords: variable
AACSB: Analytic skills
6) Parameters are known, constant values that are usually coefficients of variables in equations.
Answer: TRUE
Diff: 1 Page Ref: 3
Section Heading: The Management Science Approach to Problem Solving
Keywords: parameter
AACSB: Analytic skills
7) Data are pieces of information from the problem environment.
Answer: TRUE
Diff: 1 Page Ref: 4
Section Heading: The Management Science Approach to Problem Solving
Keywords: data
AACSB: Analytic skills
8) A model is a mathematical representation of a problem situation including variables, parameters, and equations.
Answer:...

...ORGANISING YOUR DATA:
A. Summarise your results in a table.
Name
Age
Writing Hand R/L?
Writing hand angle
Non-writing hand angles
Right (√)
Left (√)
Zac Taylor
15
√
50o
50o
Eric Na
17
√
55o
52o
Damian Bielinski
15
√
49o
48o
Ashley Vandenput
15
√
47o
50o
Tolga Pasin
15
√
50.5o
53o
Corey Evans
15
√
52o
50o
Romy Abbott
14
√
50o
53o
Candice Shadford
15
√
45o
54o
Jess Dayus
14
√
50o
55o
Joel Dayus
11
√
49o
55o
Myriam Dayus
42
√
58o
45o
Toby Abbott
16
√
53o
52o
B. Arrange your data in numerical order.
C. Calculate the five number summaries and summarise this information in a table.
D. ANALYSING THE DATA:
a) Select three (3) categories from those above and construct parallel box plots from your five number summaries.
b) Provide printouts of the three parallel boxplots.
E. Write a 300 word (approx) detailed analysis of the parallel boxplots.
Twelve people were tested on the angles of their writing and non-writing hand. These people aged through from eleven (11) to forty two (42), the data obtained was put into tables and a box plot diagram. A box plot is a diagram used to represent the range, median and quartiles of a set of data values. The difference between males and females will be compared, along with the shape of distribution of the diagram and the range. The three sets of data that were chosen to compare...

...
Ayivi Koutodjo
Case Assignment3
Professor Erickson
Liberty University
BUSI 600- B02
September 7, 2014
Case Assignment3: Surveys
Communication approach is a critical step in a business research. It involves surveying or interviewing people and recording their responses for analysis (Cooper & Schindler, 2013, pg. 218). Despite its disadvantages, surveys have gained in popularity. Nevertheless, surveys need a good planning, which would ultimately lead to an excellent analysis.
Critique the survey used for the study
In this case, “Inquiring Minds Want to Know ---Now!” (Schindler & Cooper, 2011), Penton Media relied on self-administered survey to gather information from subscribers. The questionnaire is sent to subscribers through mail. The basic concept of survey research involves capturing beliefs, attitudes, or outcomes that can be generalized to a population from which the sample was selected (Alderman & Salem, 2010, pg. 1381). Self-administered survey allows enough time for participants to complete the survey. In addition, it enables Penton Media to maximize participation as subscribers could include more...

...Julia’s Food Booth
Based on the LP model to maximize profit with the established constraints Julia should sell pizza and hotdogs and not BBQ sandwiches. Based on this model Julia will earn $2250.00 in profit. After buying food supplies for the next game she will have $750 remaining ($2250-1500). Julia’s goal was to clear $1000 in profit which she was not able to meet. It is not clear how Julia is paying for the booth rental each game, but assuming she is covering the costs with her profits from the prior game she will need $1000 for the booth + $1500 for food which equals $2500 she needs to make each game just to cover her expenses.
The idea of Julia borrowing money would not be necessary because what is limiting her profit is the limited space she has in the oven. In the model all of the oven space is being utilized by Pizza and Hotdogs. If she borrowed money she wouldn’t have enough room to stock more food. She would have to borrow enough money to rent another oven, if there was enough space in the booth, and enough money to buy additional supplies. In addition, assuming that my calculations are correct paying a friend to help her does not seem like a good idea as it would further cut into any profit and increase costs.
There are many uncertainties that can affect Julia’s profit. The case states that Julia anticipates selling all of her food; but not selling out will adversely affect her already strained profit margin. Fluctuations in the cost of the...

...motion of the body. The presence of friction between contact surfaces generates sound, light, and heat energy. It is also referred to as the retarding force or even drag force in the form of air resistance.
Frictional force is found to be directly proportional to the normal force (N) which is mathematically expressed as:
f ∝N
f=kN (Equation 1)
The coefficient of friction (µ) takes the place of k which is the constant of proportionality. Thus:
f=µN (Equation 2)
26904953626485Figure3. Angle of Repose
Figure 3. Angle of Repose
269061011472000If the body slides down the incline due to its own weight, the angle between the horizontal and the incline is called angle of repose 𝜽, as shown in Figure 3. In the previous experiment, if we are measuring along the y-axis, the formula will be
ΣFy=0, f=Wcosθand if we are measuring along the x-axis, the formula will be
ΣFx=0, f=Wsinθ.
The coefficient of friction is equal to the tangent of the angle of repose.
µ=fN=WsinθWcosθ, µ=tanθ(Equation 3)
In this experiment, we should be able to determine the coefficient of friction (µ) between contact surfaces as one body moves with uniform motion and establish the relationship between the angle of repose (𝜽) and µ. The rules of this experiment are to keep clean the surfaces of the wooden block and plane by wiping them with a piece of scratch paper or tissue to remove dust and other particles and to make sure not to touch the...