Teneika Smith
Strayer University
Professor Guo
Julia’s Food Booth Assignement #3

A. Formulate and solve an L.P. model for this case.
x1=slices of pizza
x2= Hot Dogs
x3= Barbecue Sandwiches
Maximize, Z= $0.75x1+ $1.05x2+$1.35x3
Constraints:
$0.75x1+$0.45x2+$0.90x3 < = $1500 (cost)
24x1+16x2+25x3< = 55,296 square inches (Oven Space)
***14 x 14 = 196 inches squared 196/8= 24.5. The total space available is 36 in. x 48 in. = 1,728 inches squared Then 1728 is multiplied by 16= 27,648 in2, which is multiplied by 2 totaling 55, 296 square inches***

x1-x2-x3 > = 0 (at least as many slices of pizza as hot dogs and barbecue sandwiches) x2-2x3> = 0 (at least twice as many hot dogs as barbecue sandwiches Non negative constraints
x1, x2, x3 are all > = 0

x1= $1250
x2=$1250
x3=$ 0
Julia’s profit for the first game should be $2, 250. The prices of the booth lease is $1000 per game and the oven lease is $600 for the six game season therefore the lease for the oven is $100 per game decreasing her first game profit to $1150. B. Evaluate the prospect of borrowing money before the first game. Based on the results of the linear programming model in QM the dual value is $1.50. “The dual value measures the increase in the objective function’s value per unit increase in the variable’s value” (Frontline Solvers, 2012). Borrowing money before the first game would increase Julia’s profit. The dual value is $1.50 for every additional dollar. C. Evaluate the prospect of paying a friend $100 per game to assist Julia would benefit from hiring an additional friend to assist her because having another person will allow her to make more money because she could more than likely make all the food required to reach maximum profit. D. Analyze the impact of uncertainties on the model.

There are a couple of factors that come to mind when thing about what could affect the sales. For example, the weather could create a problem for...

...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 |...

...Julia’sFoodBooth Case Problem
MAT 540- Quantitative Methods
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
X2X3≥2.0
X1, X2, X3≥0
(B) Evaluate...

...Julia’sFoodBooth Case Problem
Assignment 3
Max Z =Profit1x1+ Profit2x2+ Profit3x3
A - Formulation of the LP model
x1 - number of pizza slice
x2 - number of hot dogs
x3 - number of barbecue sandwiches
Constraints
Cost
Maximum fund available for food = $1500
Cost per pizza $6 ÷08 (slices) = $0.75
Cost for a hot dog = $0.45
Cost for a barbecue sandwich = $0.90
Constraint: 0.75x1+0.45x2+0.90x3 ≤1500
Oven space
Space...

...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...

...(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...

...pizza, 1250 hot dogs and no barbecue sandwiches.
Maximum Profit = $2250.
|Maximum Profit 2250
Booth Rent per game 1000
Warming Oven 600 for total of 6 games 600/6 =100 for 1 game
2250-1000-100=1150 is the profit after paying all the expenses.
*I think she should lease the booth
B) the amount of Borrowing money that will increase her profit is defined by the upper limit...

...Julia’sFoodBooth
Strayer University
Quantitative Methods – MAT 540/ Spring 2012
Dr. Buddy Bruner
May 19, 2012
A) Formulate and solve an L.P. model for this case.
[pic]
[pic]
B) Evaluate the prospect of borrowing money before the first game.
After observing the ranging chart calculations indicate that the upper bound in the budget is...