Julia's Food Booth

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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:



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P >= H+B

H >= 2B


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


5

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:


P >= H+B

H >= 2B



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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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Documents

Julia's Food Booth