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Assignment 3: Julia’s Food Booth Case Problem
A.
Formulate and solve a linear programming model for Julia that will help you to advise
her if she should lease the booth.
By Formulating the model for the first home game, the profit
function and constraints and calculations is broken down to the equations.
Let, X1 =No of pizza slices,
X2 =No of hot dogs,
X3 = barbeque sandwiches
Formulation:
1. Calculating Objective function coefficient:
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 insquare
•
Space required for a pizza=14*14=196 insquare
Space required for a slice of pizza=196/8=24 insquare approximately.
Therefore, Objective function for the model can be written as:
Maximize Total profit Z = $0.75X1 + 1.05X2 +1.35X3
Subject to constraints:
1
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View Full Document Assignment 3: Julia’s Food Booth Case Problem
$0.75X1 + .0.45X2 + 0.90X3 <= 1,500 (Budget constraint)
24X1 + 16X2 +25X3 <= 55,296 (Inch square Of Oven Space)
X1>=X2 + X3 (at least as many slices of pizza as hot dogs and barbeque sandwiches combined)
X2/X3>= 2.0
(at least twice as many hot dogs as barbeque sandwiches)
This constraint can be rewritten as:
X22X3>=0
X1, X2, X3 >= 0
Final Model:
Maximize Total profit Z = $0.75X1 + 1.05X2 +1.35X3
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This note was uploaded on 06/05/2011 for the course MAT MAT540 taught by Professor Subhashis during the Spring '10 term at Strayer.
 Spring '10
 SUBHASHIS
 Linear Programming

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