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DECISION MODELLING AND OPTIMIZATION
Julia’s Food Booth
Case Study Analysis
Submitted To: Dr. R. Jagadeesh Date of Submission: 13-02-2015
Submitted By: Section ‘A’ / Group – 3
Name PGDM No.:
Aishwarya B 14008
Bishal Guha 14036
Dileep Reddy 14090
Ravikiran R 14118
SIrsha Mondal 14155
Venkatesh Kamath 14175
Executive Summary
Julia is a senior at Tech, and she’s investigating different ways to finance her final year at
school. She is considering leasing a food booth outside the Tech stadium at home football
games. She is thinking to sell items such as:
1) cheese pizza
2) hot dogs
3) barbecue sandwiches
If Julia clears at least $1,000 in profit for each game after paying all her expenses, she
believes it will be worth leasing the booth. She wants to formulate a linear programming
Decision Modelling & Optimization SDMIMD
Check list Included1.Title page 2. Executive Summary 3. Statement of the problem 4. Causes of the problem 5. Decision criteria & alternative solution
6. Recommended solution 7. End of case questions 8. References
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model that will help her in decision of leasing the booth for the first home game. Her
objective is to derive the profit function.
Statement of the problem
The main Dilemma in the case is to find out in which way she will get the maximum profit by
selling the items. Whether it will be a single item, a combination of two items or all three
products together.
She has $1,500 in cash available to purchase and prepare the food items for the first home
game and for the remaining five games she will purchase her ingredients with money she has
made from the previous game. From this she has discovered that she can expect to sell at least
as many slices of pizza as hot dogs and barbecue sandwiches combined. She also anticipates
that she will probably sell at least twice as many hot dogs as barbecue sandwiches. If Julia
clears at least $1,000 in profit for each game after paying all her expenses, she believes it will
be worth leasing the booth.
Cause of the Problem
The main condition she has to consider is that she has to fetch her total revenue over $2100 as
she has a Fixed cost of 1100 and her profit have to be more than $1000. According to this
condition she has to decide whether she should go for the lease or not.
Decision criteria and alternative solution
Based on the constraints and formation of the question she is going to decide to lease the
booth or not.
Total area: 36*48 = 1728 Sq. inches
Let P = Number of Pizza Slices
H = Number of Hot Dogs
B = Number of Barbecue Sandwiches
Individual Area:
Pizza = 196 Sq. inches; Hot dog = 16 Sq. inches
Barbecue Sandwich - 25 Sq. inches
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Formulation:
To find area of Pizza slice:
Total area: 14*14 = 196 inches square
For each slice: 196/8 = 24 inches per slice
Similarly the given areas for
1. Hot dogs: 16 square inches
2. Barbecue Sandwiches = 25 square inches
H= No. of Hot dogs; P= No. of Pizza slices; B= No. of barbeque sandwiches.
Objective Function:
Maximise Z = $0.75P +$ 1.05 H +$1.35 B
Constraints:
24P + 16H + 25B <= 55,296 square inches
P >= H+B
H >= 2B
and Non- negative constraints : P, B & H >= 0
Recommended solution, Implementation and Justification
Model used: Solver method
Decision variables:
Let P = Number of Pizza Slices
H = Number of Hot Dogs
B = Number of Barbecue Sandwiches
Objective Function:
Maximise Z = $0.75P +$ 1.05 H +$1.35 B
Constraints:
24P + 16H + 25B <= 55,296 square inches
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P >= H+B
H >= 2B
and Non- negative constraints : P, B & H >= 0
P H B LHS
CONSTRAIN
T RHS
24 16 25 50000 <= 55296
0.75 0.45 0.9 1500 <= 1500
1 -1 -1 0 >= 0
0 1 -2 1250 >= 0
The optimum variables: No. of pizza slice = 1250 and No. of Hot dogs= 1250 and Barbeque
Sandwiches = 0. The profit she is earning 2250.
Answer report:
Objective Cell (Max)
Cell Name
Original
Value Final Value
$E$5 profit 2250 2250
Variable Cells
Cell Name
Original
Value Final Value Integer
$E$4
variabl
e 1250 1250 Contin
$F$4
variabl
e 1250 1250 Contin
$G$4
variabl
e 0 0 Contin
Constraints
Cell Name Cell Value Formula Status
Slac
k
$G$1
1 LHS 0
$G$11>=$I$
11 Binding 0
$G$1 LHS 1250 $G$12>=$I$ Not 1250
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2 12 Binding
$G$9 LHS 50000 $G$9<=$I$9
Not
Binding 5296
$G$1
0 LHS 1500
$G$10<=$I$
10 Binding 0
Sensitivity Analysis:
Variable Cells
Fina
l
Reduce
d
Objectiv
e
Allowab
le Allowable
Cell Name
Valu
e Cost
Coefficie
nt Increase Decrease
$E$4
variabl
e 1250 0 0.75 1 1
$F$4
variabl
e 1250 0 1.05 1E+30
0.2727272
73
$G$4
variabl
e 0 -0.375 1.35 0.375 1E+30
Constraints
Fina
l
Shado
w
Constrai
nt
Allowab
le Allowable
Cell Name
Valu
e Price R.H. Side Increase Decrease
$G$1
1 LHS 0 -0.375 0 2000
3333.3333
33
$G$1
2 LHS 1250 0 0 1250 1E+30
$G$9 LHS
5000
0 0 55296 1E+30 5296
$G$1
0 LHS 1500 1.5 1500 158.88 1500
Limits Report:
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Objecti
ve
Cell Name
Valu
e
$E$
5 profit 2250
Variabl
e
Low
er
Objecti
ve
Upp
er
Objecti
ve
Cell Name
Valu
e
Limi
t Result
Limi
t Result
$E$
4 variable 1250 1250 2250 1250 2250
$F$
4 variable 1250 0 937.5 1250 2250
$G$
4 variable 0 0 2250 0 2250
End-of-case question
Question A: Formulate and solve a linear programming model for Julia that will help
you advise her if she should lease the booth.
Solution:
Objective Function
Maximise Z = $0.75P +$ 1.05 H +$1.35 B
Constraints:
24P + 16H + 25B <= 55,296 square inches
P >= H+B
H >= 2B
and Non- negative constraints : P, B & H >= 0
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She makes a profit of $2250. She makes use of: 1000 + 100 = $1100. Therefore: $2250 -
$1100 = $1150. Therefore, we advise her to lease the booth.
Question B: If Julia were to borrow some more 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 additional profit would she make? What factor
constrains her from borrowing even more money than this amount (indicated in your
answer to the previous question)?
Solution From the report it can be seen that, the Shadow price for the budget constraint is 1.5
and the allowable increase is 158.88. This means that each dollar added to the budget can
increase a profit of $1.5 and the maximum allowable increase is 158.88. So maximum
amount that Julia can borrow from her friend to make profit is $158.88 and it will make an
additional profit of 158.88 x 1.5 = 238.32.
Question C: When Julia looked at the solution in (A), she realized that it would be
physically difficult for her to prepare all the hot dogs and barbecue sandwiches
indicated in this solution. She believes she can hire a friend of hers to help her for $100
per game. Based on the results in (A) and (B), is this something you think she could
reasonably do and should do?
Solution: If Julia hires a friend to help her for $100 per game, her net profit per game will be
1150-100 = $1050. Still, as per her strategy, it is worth leasing the booth. Hence, she should
hire her friend if it is physically difficult for her to prepare the required quantity of hot dogs.
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Question D: Julia seems to be basing her analysis on the assumption that everything will
go as she plans. What are some of the uncertain factors in the model that could go
wrong and adversely affect Julia's analysis? Given these uncertainties and the results in
(A), (B), and (C), what do you recommend that Julia do?
Solution: The main uncertain factor is demand. She believes that she will sell everything she
can stock and develop a customer base for the season. If this is violated, then nothing would
work.
As per result in (A), the net profit she can earn is $1150. It is above her target $1000.
Hence, she can earn a profit of $150/- within her target.
As per result in (B), if she borrows money from her friend of $158.88, she will earn a
profit of $1387 ( $2487 - $1100) where she will be selling 1381 pizza slices and 1381
hot dogs.
Now, as per the result in (C), if she hires a friend to help her $100 per game, she will
be earning a profit of $1050 as shown above and the threshold limit for her
preparation of hot dogs is 1108, which is the breakeven. (if she prepares less than
1108, she will be under loss) and we aren’t sure whether she will be able to prepare
1108 hot dogs by herself. So, it’s better to hire a friend which will help her to make
profit.
References
Balakrishnana, N., Render, B., & Stair, R. M. (2013). Managerial Decision Modeling with
Spreadsheets. Pearson.
Render, B., Stair, R. M., & Hanna, M. E. (n.d.). Quantitative analysis for management.
Taha, H. A. (2006). Operations research: An Introduction.
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Decision Modelling & Optimization SDMIMD