Shannon's Food Booth" case problem Name

Formulate and solve an L.P. model for this case.

1. Decision Variables

X1 = Number of Pizzas Slices

X2 = Number of Hot Dogs

X3 = Number of Hamburgers

2. Objective Function

The profit for a pizza slices = $1.50 - $0.75 = $0.75

The profit for a single hot dog = 1.50 – 0.45 = $1.05

The profit for a single sandwich = 2.25 – 0.90 = $1.35

The profit for the objective function, Z, is thus 0.75 X1 + 1.05X2 + 1.35X3

3. Constraints

Oven Size

24 * 1 + 16 * 2 + 25 * 3 = $1250

Demand for Hot Dogs

X2>= 1250

Solution

B. The prospect of borrowing before the first game.

Target Cell (Max)

Cell

Name

Original Value

Final Value

$E$3

Profit Total

2250

2250

Adjustable Cells

Cell

Name

Original Value

Final Value

$B$10

X1

1250

1250

$C$10

X2

1250

1250

$D10

X3

0

Constraints

Cell

Name

Cell Value

Formula

Status

Slack

$E$4

Space Constraint

50625

$E$4=0

Not Binding

1250

$E$10

X3

0

$D$10>=0

Binding

0

For us to determine the prospect of borrowing for the first time, we use Excel to find the sensitivity report as shown below.

Final

Reduced

Objective

Increase

Allowable

Cell

Name

Val.

Cost

Coeff.

allowable

Decrease

$B$10

X1

1250

0

0.75

1

1.00000001

$B$10

X2

1250

0

1.05

1E + 30

0.272727279

$B$10

X3

0

-0.38

1.350000002

0.375000011

1E + 30

Final

Shadow

RHS

Allowable

Allowable

Cell

Name

Val.

Price

Constraint

Increase

Decrease

$B$4

Space

50625

0

55296

1E + 30

4671

$B$5

Budget

1500

1.5

1500

138.4

1500

$B$6

Demand 1

0

-0.375

0

2000

3333.333333

$B$7

Demand 2

1250

0

0

1250

1E + 30

From the report, the shadow price for price constraint is $1.5 while the allowable increase is 138.4. That means if Shannon adds a dollar to the budget she can gain a profit of $1.5 and have a maximum gain of up to 138.4. Therefore, the maximum amount that Shannon needs to borrow from a friend is $138.4. She will also make a surplus profit of 138 * 1.5 = $207.6.

C. Evaluate the prospect of paying a friend $150/game to assist.

Should Shannon hire a friend to assist her at a cost of $150 per game, her net profit in a single game will amount to 1150 – 150 = $1000. That shows that as per her strategy, she can lease the booth still. Should Shannon find it difficult to prepare all the food within the available time, it will be prudent for her to hire a friend.

D. Analyze the impact of uncertainties in the model

The major uncertainty factor that Shannon should take into consideration is demand. Shannon has the tenet that if she sells everything that she prepares she will be able to meet her vision. If things fall apart, and she fails to sell as much as she has, everything will collapse. The net profit that the lady can earn is $1150 and she if she hires a friend it drops to $1000, and she has to hire because of the heavy workload that would be hard when she does it alone. If Shannon has to sustain a high profit, she will need to do away with some of the hotdogs and by so doing she will reduce the uncertainty of the demand.

Sherry Roberts is the author of this paper. A senior editor at Melda Research in Buy Term Papers Online if you need a similar paper you can place your order for a custom research paper from Custom Research Paper Writing.

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