Introduction
Julia is planning to lease a food booth outside the Tech Stadium at Home Football games to finance her last year education with all the games go sold out. The rent for the booth per game is $ 1000. Julia will sell slices of Cheese Pizza, Hot Dogs and Barbecue Sandwiches which are acclaimed to be the most popular so these are the three products she has chosen to sell at the home games football stadium. The rent for oven is $ 600 for six home games, which makes it $ 100 per game. To keep things simple, Julia decided to hire an outside pizza delivery company, it seems to be cost effective and for other items she plans to prepare them the night before. Space taken by Pizza is 14” x 14”, hot dogs are 16 in/sq. and the BBQ sandwich is 25 “sq. The cost price of Pizza $6.00, or $.75 ea slice with 8 slices/pizza the hot dogs $0.45 each, and sandwiches$.90 each, respectively. The sale price of Pizza Slice is $1.50, hot dogs $1.60 and the BB-Q sandwich is $2.25. Julia’s initial investment is $1500 which would pay for the first game day; she would pay the future home games out of proceeds earned from the games. From Student Feedbacks she has learnt that she can sell as many slices of Pizza as Hot dogs and BBQ sandwich’s combined. She feels she can sell twice as many hot dogs as she can the BBQ sandwich’s. Julia believes that she can make at least $1000 net profit after expenses are paid per game. Objective Function

Objective here is to maximize the profit. Profit is calculated for each variable by subtracting cost from the selling price. Pizza. Cost $6 / 8 = $ 0.75 (Cost per slice) Z =$0.75 x1 +$.45x2 + $.90 x3. Profit per: $.75/slice pizza, $1.15/hot dog $ 1.35/BBQ Sandwich Sales Price: $2.25 $ 1.60 $ 1.50 Sale Price: 3x/Sandwich; 2x/ Hot dog and 1x/pizza slice. Decision Variables Constraints:

Budget Constraint:
0.75x1 + 0.45x2 + .90x3 2x3
x2 – 2x3 => 0
If extra help @$100/game = $100/x6
Non...

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Julia’s FoodBooth
(A) Formulate and solve an LP model for this case
The objective here is to maximize the profit. Profit is calculated for each variable by subtracting cost from the selling price. The decision variables used are X1 for pizza slices, X2 for hotdog, and X3 for BBQ sandwich.
X1 (pizza)
X2 (hotdog)
X3 (sandwich)
Sales Price
1.50
1.50
2.25
Cost
0.75
0.45
0.90
Profit
0.75
1.05
1.35
*For Pizza Slice: Cost/Slice = $6/8 = $0.75 cost per slice
Maximize Z = 0.75 X1 + 1.05 X2 + 1.35 X3
Constraints:
Budget: 0.75X1 + 0.45X2 + 0.90X3 ≤ 1500
Oven Space: 24X1 + 16X2 + 25X3 ≤ 55,296 in2
The calculation for the oven space is as follows:
Pizza slice total space required for a 14 * 14 pizza = 196 in2. Since there are eight slices, we divide 196 by eight, and this gives us approx. 24 in2 per slice.
The total dimension of the oven is the dimension of the oven shelf, 36 in * 48 in = 1728 in2, multiplied by 16 shelves = 27,648 in2, which is multiplied by 2, before kickoff and during the halftime, giving a total space of 55,296in2.
(B) Evaluate the prospect of borrowing money before the first game.
The shadow price or dual value is $1.50 for each additional dollar Julia would increase her profit, if she borrows some money. However, the upper limit of the sensitivity range is $1,658.88, so she should only borrow $158.77 and her additional profit would be $238.32 or a total profit of...

...H=HOTDOGS
S=BARBEQUE SANDWHICHES
The L.P. for this case is,
Maximize:
P= 0.75P +1.05H +1.35S
Subject to:
24.5p +16h +25s ≤ 55296
0.75p + 0.45h+0.90s ≤ 1500
P – h – s ≥ 0
H - 2s ≥ 0
P , h , s ≥ 0
The optimal solution occurs when
P=1250
h-1250
s=0
Profit =$2250
Since the booth costs $1000 to lease per game, and the oven is $100 per game, then Julia's overall profit is,
P = 2250 - 1100 = $1150
Hence it is worth leasing the booth.
b) The shadow price for the budget is 1.50 and allowable increase is 138.4 Therefore, each dollar added to the budget will increase profit by $1.50 with a maximum increase of $138.40. Therefore the maximum amount Julia can borrow is $138.40 which will produce an additional profit of 138.4 x 1.5 = $207.60. Space is the factor which constrains Julia from borrowing more money.
c)
If Julia feels she needs help than $100 would still keep her above the $1000 dollar profit margin. Therefore, if Julia cannot handle the work load alone it would be advisable for her to hire some help. If she is able to handle the work load herself, then she could keep that $100 for herself.
d)
The biggest uncertainty in this model is demand. Although Julia may have a good idea of what people will buy and not buy during the game, the demand can shift from game to game and is not always constant. Hence, if the demand changes then the...

...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)
[pic]
[pic]
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...

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JuliaBooth Case Study
Angela Walker
June, 06, 2013
Dr. Carl Tucker field
In this case study, I must create a linear programming model for Julia that will help her to decide whether or not she need to lease a booth. The three products or variable we must consider for this booth are pizza, hotdogs, and barbecue sandwiches. In this model, x 1 equal the number of pizza slices Julia should purchase, x2 equals the number of hotdogs Julia should purchase, and x3 equal the number of barbecue sandwiches Julia should purchase. The objective is to maximize total profit and the way to do that is to calculate each variable by subtracting cost from the selling price. For instance, if the pizza cost six dollar for eight slices then that mean she is only paying seventy-five cent for pizza and to make her money back she need to sell them for $1.50.
If she borrow money from a friend before the first game to purchase more ingredients, could she increase her profit? If so, how much should she borrow and how much will she make? What factor constrains her from borrowing even more money than this amount? By looking at the model, it tells us that she can increase her profit if she borrow the money from her friend.by looking at the sensitivity analysis report it tells us that she will make $1.50 for every dollar she borrow she will make a $1.50 in return. The price seem well within...

...Food in Your Life
Topic Review
Complete topic review. Put the answers in a different color.
List the 4 key behaviors for wellness.
1. Positive food choices
2. Physically active
3. Managing stress
4. Alcohol/drug free
Explain the role of science in food.
Science tells you what nutrients do in your body and how nutrients work together
Explain why people who enjoy their food may absorb more nutrients from it.
The brain reacts from the senses (sight and smell). It instructs your mouth and stomach to make chemicals that help digest food.
What 5 factors contribute to different cultures having such different cuisines and food customs?
Geography, Economics, Foreign Contacts, Religious Belief, Technology.
List the 4 main components of the food chain and explain the function of each.
Sun: The sun supplies the original energy for the planer in the form of light. This energy is needed to make food.
Producers: Some organisms make or produce food. Green plants are important producers. Plants use the sun’s energy to produce food for themselves.
Consumers: Organisms that must eat other organisms.
Decomposers: Organisms such as bacteria and fungi that break down dead matter and return the nutrients to the environment.
List the 5 reasons for using food additives.
1. Additive flavoring
2. Improving nutrition...

...Foods to avoid:
We asked Food Scientists a simple question: “What foods do you avoid? Experts from different areas of specialty explain why they won’t eat these eight foods.
Food scientists are shedding light on items loaded with toxins and chemicals–and simple swaps for a cleaner diet and supersized health. Experts from different areas of specialty explain why they won’t eat these eight foods.
Clean eating means choosing fruits, vegetables, and meats that are raised, grown, and sold with minimal processing. Often they’re organic, and rarely (if ever) should they contain additives. But in some cases, the methods of today’s food producers are neither clean nor sustainable. The result is damage to our health, the environment, or both. So we decided to take a fresh look at food through the eyes of the people who spend their lives uncovering what’s safe–or not–to eat. ” Their answers don’t necessarily make up a “banned foods” list. But reaching for the suggested alternatives might bring you better health–and peace of mind.
1. The Endocrinologist Won’t Eat: Canned Tomatoes
Fredrick Vom Saal, is an endocrinologist at the University of Missouri who studies bisphenol-A.
The problem: The resin linings of tin cans contain bisphenol-A, a synthetic estrogen that has been linked to ailments ranging from reproductive problems to heart disease, diabetes,...

...Julia’s FoodBoothJulia Robertson is a senior at Tech, and she's investigating different ways to finance her final year at school. She is considering leasing a foodbooth 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 to pay $1,000 per game for 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.
Most food items are sold during the hour before the game starts and during half time; thus it will not be possible for Julia to prepare the food while she is selling it. She must prepare the food ahead of time and then store it in a warming oven. For $600 she can lease a warming oven for the six-game home season. The oven has 16 shelves, and each shelf is 3 feet by 4 feet. She plans to fill the oven with the three food items before the game and then again before half time.
Julia has negotiated with a local pizza delivery...