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 solution to the linear programming will change, and may affect her ability to make a profit greater than $1000.

...JuliaFoodBooth
Introduction
Julia is planning to lease a foodbooth 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...

...
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...

...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...

...(A) Formulate and solve an L.P. model for this case
Variable Food Cooking Area
x1 Pizza Slice 24in sq
x2 Hot Dogs 16in sq
x3 BBQ Sandwiches 25in sq
*The oven space required for a pizza slice is calculated by dividing the total area arequired for a whole pizza by the number of slices in a pizza 14 x 14 = 196 in2, by 8, or approximately 24 in2 per slice. The total space available is the dimension of a shelf, 36 in. x 48 in. = 1,728 in2, multiplied by 16 shelves, 27,648 in2, which is multiplied by 2, the times before kickoff and halftime the oven will be filled = 55,296 in2.
Maximize Z = $0.75x1 + 1.05x2 + 1.35x3
Subject to:
$.75x1 + $.45x2 + $.90x3≤1500
24x1 + 16x2 + 25x3 ≤ 55296in sq of oven space
x1 ≥ x2 + x3
x2/x3 ≥ 2
x1,x2,x3 ≥ 0
Solution:
X1 = 1250 slices of pizza
X2 = 1250 hotdogs
X3 = 0 BBQ sandwiches
Julia would profit $2250. Her lease per game for the tent is $1000.00 and $100.00 for the warming oven. This means she still clears $1150 which is more than her $1000 minimum profit to open the concession stand.
(B) Evaluate the prospect of borrowing money before the first game.
Julia should borrow money based on the given scenario. She could increase her profit if she borrows money from a friend. The shadow price, or dual value, is $1.50 for each extra dollar that she earns. The upper limit given in the model is $1,658.88. This means that she would max out her profit at $1,658.88 of spending....

...Julia’s FoodBooth
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 |
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.
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 her borrowing the extra $158.88 from her friend, Julia would be able...

...
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...