Assignment 3: Case problem “Julia’s Food Booth” Page 1 A. Julia Robertson is making an allowance for renting a food booth at her school. She is seeking ways to finance her last year and believed that a food booth outside her school’s stadium would be ideal. Her goal is to earn the most money possible thus 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 boot. 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) X1, X2, X3 ≥ 0
Solution:
Variable | Status | Value |
X1 | Basic | 1250 |

Assignment 3 Case problem “Julia’s Food Booth” Page 2 X2 | Basic | 1250 |
X3 | NON Basic | 0 |
Slack 1 | NON Basic | 0 |
Slack 2 | Basic | 5296.0 |
Slack 3 | NON Basic | 0 |
Slack 4 | Basic | 1250 |
Optimal Value (Z) | | 2250 |
Built on the above LP model, Julia is estimated that she will earn a profit of $2,250.00. After paying for the rental lease, she has earned a net profit of $1,250.00. The model suggests that she rents the booth and sell only pizza and hotdog due to her spacing constraints. This is Julia best optimal results. B. Evaluate the prospect of borrowing money before the first game. In my opinion if Julia borrowed more money she could increase her profit. Any change in a coefficient in a parameter is carefully analyzed using sensitivity analysis. This analysis identifies any effect an independent variable might have on Julia’s given constraints, in this case her budget. The increase will generate an increase in product availability...

...(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...

...Complete the "Julia'sFoodBooth" case problem on page 109 of the text. Address each of the issues A - D according the instructions given.
(A) Formulate and solve an L.P. model for this case.
(B) Evaluate the prospect of borrowing money before the first game.
(C) Evaluate the prospect of paying a friend $100/game to assist.
(D) Analyze the impact of uncertainties on the model.
The assignment will be graded using the associated...

...Julia’sFoodBooth
Julia 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...

...A. Formulate a linear programming model for Julia that will help you to advise her if she should lease the booth.
Let, X1 =No. of pizza slices,
X2 =No. of hot dogs,
X3 = No. of barbeque sandwiches
* Objective function co-efficient:
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=$4.5/6=$0.75
| X1 | X2 | X3 |
SP | $1.50 | $1.60 | $2.25 |
-Cost | 0.75 |...

...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...

...stock 1250 slices of pizza and 1250 numbers of Hot dogs. She need not stock sandwiches.
Maximum Profit that can be expected is $2250.
Lease cost for the booth per game = $1000
Lease cost for the oven per game = $100
Net profit after all the expenses = 2250 – 1100 = $1150
Now it is clear that as per the strategy it is worth leasing the booth.
B) The sensitivity report of the solution is given below
| | | ...

...Julia’sFoodBooth Case Problem
MAT 540- QuantitativeMethods
February 23, 2013
(A) Formulate and solve an L.P. model for this case.
The following variables were be used:
X1 = Slices of Pizza
X2 = Hot Dogs
X3 = BBQ Sandwiches
The objective is to maximize profit.
maximize Z= 0 .75X1+1.05X2+1.35X3
Subject to:
0.75X1+1.05X2+1.35X3≤1,500 (Budget)
24X1+16X2+25X3≤55,296in2 (Oven Space)
X1≥X2+X3...