Julia’s Food Booth
Strayer University
Quantitative Methods MAT 540
December 12, 2012
Dr. L. Joseph

Introduction

Julia is a senior at Tech, and she’s investigating different ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game, and Julia knows, from attending the games herself, 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. 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.

If Julia clears at least $1,000 in profit for each game after paying all her expenses, she believes it will be worth leasing the booth.

A. Formulate a linear programming model for this case.

Decision Variables

Representing “x1” as pizza slices, “x2” as hot dogs, and “x3” as barbeque sandwich

The Objective Function

The objective is to maximize total profit. Profit is calculated for each variable by subtracting cost from the selling price.

...A. Julia Robertson is considering renting a foodbooth at her school. She is seeking ways to finance her last year and thought that a foodbooth outside her school’s stadium would be ideal. Her goal is to earn the most money possible thereby increasing her earnings. In this case problem, she decided to sell pizza, hotdogs and BBQ sandwiches. The following LP model illustrates the maximum net profit and constraints that will determine whether or not to least the booth.
Z = $ .75(X1) + $1.05(X2) + $1.35(X3)
Given the following remains true:
$ .75(X1) + $1.05(X2) + $1.35(X3) =0
and,X2/X3 >=2; Solve for 0 for Excel: X2 >= 2(X3); X2 – 2(X3)>=0
Where X1, X2, and X3 are Pizza, Hotdog and BBQ Sandwiches respectively and are greater than 0.
Based on the above LP model, Julie is expected to earn a profit of $2,250.00. After paying for rental lease, she has earned a net profit of $1250.00. The model suggests that she rents the booth and sell only pizza and Hotdog due to her spacing constraints. This will be the best option to achieve optimal results.
B. If Julia were to borrow more money to purchase more ingredients this would change her above profit. Any change in a coefficient in a parameter is carefully analyzed using a sensitivity analysis. This analysis identifies any effect an independent variable might have on Julia’s given constraints, in this case, her budget. This...

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MAT540 MIDTERM EXAM
1. Deterministic techniques assume that no uncertainty exists in model parameters.
2. A continuous random variable may assume only integer values within a given interval.
3. A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.
4. A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches.
5. A table of random numbers must be normally distributed and efficiently generated.
6. Starting conditions have no impact on the validity of a simulation model.
7. The Delphi develops a consensus forecast about what will occur in the future.
8. Qualitative methods are the least common type of forecasting method for the long-term strategic planning process.
9. Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. What time is exceeded by approximately 75% of the college students when trying to find a parking spot in the main parking lot?
10. __________ is a measure of dispersion of random variable values about the expected value.
11. The __________ is the maximum amount a decision maker would pay for additional information.
12. Developing the cumulative probability distribution helps to determine
13. Consider the...

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MAT540 MIDTERM EXAM
1. Regret is the difference between the payoff from the best decision and all other decision payoffs.
2. Variable costs are independent of volume and remain constant.
3. Regret is the difference between the payoff from the
4 A _________ period of real time is represented by a __________ period of simulated time.
5. A seasonal pattern is an up-and-down repetitive movement within a trend occurring periodically
6. A trend is a gradual, long-term, up or down movement of demand.
7. A model is a functional relationship and include
8. Random numbers are equally likely to occur.
9. Which of the following is not an alternative name for management science?
10. It's often ____________ to validate that the results of a simulation truly replicate reality.
11. ____________ moving averages react more slowly to recent demand changes than do ____________ moving averages.
12. The maximin criterion results in the maximum of the minimum payoffs.
13. ___________ is a technique for selecting numbers randomly from a probability distribution.
14. Which of the following is incorrect with respect to the use of models in decision making?
15. In computer mathematical simulation a system is replicated with a mathematical model that is analyzed
16. The maximin criterion results in the
17. Analogue simulation replaces a physical system with an analogous physical system...

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MAT540 Midterm Exam
1. Deterministic techniques assume that no uncertainty exists in model parameters.
2. A continuous random variable may assume only integer values within a given interval.
3. An inspector correctly identifies defective products 90% of the time. For the next 10 products, the probability that he makes fewer than 2 incorrect inspections is 0.736.
4. A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches.
5. Excel can only be used to simulate systems that can be represented by continuous random variables.
6. Starting conditions have no impact on the validity of a simulation model.
7. Data cannot exhibit both trend and cyclical patterns.
8. The Delphi develops a consensus forecast about what will occur in the future.
9. A company markets educational software products, and is ready to place three new products
on the market. Past experience has shown that for this particular software, the chance of "success" is 80%. Assume that the probability of success is independent for each product. What is the probability that exactly 1 of the 3 products is successful?
10. In Bayesian analysis, additional information is used to alter the __________ probability of the occurrence of an event.
11. The __________ is the expected value of the regret for each decision.
12. A seed value is a(n)
13. Random numbers generated by a...

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MAT540 Week 4 Homework
Chapter 15 problems
2. The manager of the Carpet City outlet needs to make an accurate forecast of the demand for SoftShag carpet (its biggest seller).If the manager does not order enough carpet from the carpet mill,customers will buy their carpet from one of Carpet City’s many competitors. The manager has collected the following demand data for the past 8 months:
Month Demand for Soft Shag Carpet (1,000 yd.)
1 8
2 12
3 7
4 9
5 15
6 11
7 10
8 12
a. Compute a 3-month moving average forecast for months 4 through 9.
b. Compute a weighted 3-month moving average forecast for months 4 through 9. Assign weights of 0.55,0.33,and 0.12 to the months in sequence, starting with the most recent month.
c. Compare the two forecasts by using MAD. Which forecast appears to be more accurate?
6. The manager of the Petroco Service Station wants to forecast the demand for unleaded gasoline nextmonth so that the proper number ofgallons can be ordered from the distributor.The owner has accumulated the following data on demand for unleaded gasoline from sales during the past 10 months:
Month Gasoline Demanded (gal.)
October 800
November 725
December 630
January 500
February 645
March 690
April 730
May 810
June 1,200
July 980
a. Compute an exponentially smoothed forecast, using an α value of 0.30.
b. Compute...

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MAT540 Week 2 Quiz
Question 1
If variable costs increase, but price and fixed costs are held constant, the break even point will decrease.
Question 2
Parameters are known, constant values that are usually coefficients of variables in equations.
Question 3
Probabilistic techniques assume that no uncertainty exists in model parameters.
Question 4
In general, an increase in price increases the break even point if all costs are held constant.
Question 5
P(A | B) is the probability of event A, if we already know that event B has occurred.
Question 6
A continuous random variable may assume only integer values within a given interval.
Question 7
The events in an experiment are mutually exclusive if only one can occur at a time.
Question 8
A bed and breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is $4200 per month and the revenue they receive from each booked room is $180. What their variable cost per occupied room?
Question 9
The indicator that results in total revenues being equal to total cost is called the
Question 10
If the price increases but fixed and variable costs do not change, the break even point
Question 11
A university is planning a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will...

...Final Examination
Math 540 Quantitative Methods
Good luck on the exam. I hope you have enjoyed the course. Dr. West
Multiple Choice (2 points each) (Select 8 – drop 1)
______1) For your project, what one way will not possibly generate increased profit?
a) Increase your building space or lot size.
b) Decrease the money paid to employees.
c) Refinance the loan at a lower rate.
d) Charge more for your services.
_____ 2) Which of the following is a valid objective function in linear programming?
a) Max 5xy.
b) Min 4x + 5y - (2/3)z.
c) Max 4 x 2 + 6 Y 2.
d) Min (x + y) / z.
e) None of the above.
______3) The improvement in the value of the objective function per unit increase in a right-hand side is the
a. sensitivity value.
b. shadow price.
c. constraint coefficient.
d. slack value.
_____4) Study of how changes in the coefficients of a linear programming problem affect the optimal solution is called
a. sensitivity analysis.
b. transshipment analysis.
c. sunk cost analysis.
d. duality analysis.
e. none of the above.
_____5) Which of these is not a type of integer model?
a. a real integer...

...Julia’s FoodBooth. Parts A thru C.
Please provide linear programming model, graphical solution, sensitivity report, and answers to questions A thru C. (Problem on page 2)
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A) Formulate and solve a linear programming model for Julia that will help you advise her if she should lease the booth.
Let, X1 =No of pizza slices,
X2 =No of hot dogs,
X3 = barbeque sandwiches
Formulation:
1. Calculating Objective function co-efficients:
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
| |X1 |X2 |X3 |
| SP | $ 1.50 | $ 1.50 | $ 2.25 |
|-Cost | $ 0.75 | $ 0.45 | $ 0.90 |
| | | | |
|Profit | $ 0.75 | $ 1.05 | $ 1.35 |
• Total space available=3*4*16=192 sq feet =192*12*12=27,648 in- square
The oven will be refilled during half time.
Thus, the total space available=2*27,648= 55,296 in-square
• Space required for a pizza=14*14=196 in-square
Space required for a slice of pizza=196/8=24 in-square approximately.
Thus, Objective function for the model can be...