Assignment #3: Case Problem “Julia's Food Booth”

Assignment #3: Case Problem "Julia's Food Booth"

Formulating the LP model for Julia Robertson that will certainly help to provide her the analysis that if she could lease the booth.

Assuming the variables

A =No. of pizza slices,

B =No. of hot dogs,

C = No. of barbeque sandwiches.

Linear Programming Model

Maximize Total profit Z = $0.75A + 1.05B +1.35C

Subject to the following Conditions:

24.5 A + 16 B + 25 C = 55296

0.75 A + 0.45 A + 0.90 C = 1500

A - B - C = 0

B - 2C = 0

A= 0, B= 0 and C =0

Solution

The below solution has been obtained by using the Simplex Method and the Iterations for the LP model are explained in the Appendix.

Variable

Status

Value

A

Basic

1250

B

Basic

1250

C

NON Basic

0

slack 1

Basic

4671.002

slack 2

NON Basic

0

surplus 3

NON Basic

0

surplus 4

Basic

1250

surplus 5

Basic

1250

surplus 6

Basic

1250

surplus 7

Basic

0

Optimal Value (Z)

2250

According to the above results, the entire budget Julia had was used and there is no further funds that are leftover because the slack value is zero. There is also no space available in the oven because of zero slack and therefore Julia would be having no further space for making food and thus she should not borrow funds. According to the above results by adding each dollar to the given budget of Julia will increase the profit by $1.50. This can be concluded from the results that the maximum amount which she can borrow is almost $138.40 which produces an extra profit of 138.4 x 1.5 = $207.60. The results thus say that Space is the major factor which restricts Julia from borrowing extra money.

If Julia feels that she requires help than spending $100 would still maintain Julia above the $1000 dollar profit. Thus, if she is not able to handle the work load by herself it is advised to her that she should hire someone for help. But on the other hand if she can handle the workload to her own, then she can save that $100 for herself.

Demand for the variables is the major the concern for uncertainty. Julia has an idea of the willingness of the people that they will buy it or not buy during the game. The demand for the goods can shift from game to game depending on the uncertainty and is certainly not always constant. Therefore, if the demand for the goods changes then the linear programming will certainly change, and will affect her and her abilities to make a profit more than $1000. Attendance, Weather, and food costs are the major variables that may affect her profit.

References

B. Mahadevan, (2009), Operation Management: Theory and Practice.

D. K. Mishra, (2009), Operations Management: Critical Perspectives on Business.

Saul I. Gass, (2010), Linear Programming: Methods and Applications.

Appendix

Cj

Basic Variables

.75 X1

1.05 X2

1.35 X3

0 slack 1

0 slack 2

0 artfcl 3

0 surplus 3

0 artfcl 4

0 surplus 4

0 artfcl 5

0 surplus 5

0 artfcl 6

0 surplus 6

0 artfcl 7

0 surplus 7

Quantity

Iteration 1

 

cj-zj

2

1

-2

0

0

0

-1

0

-1

0

-1

0

-1

0

-1

 

0

slack 1

24.5

16

25

1

0

0

0

0

0

0

0

0

0

0

0

55,296

0

slack 2

0.75

0.45

0.9

0

1

0

0

0

0

0

0

0

0

0

0

1,500

0

artfcl 3

1

-1

-1

0

0

1

-1

0

0

0

0

0

0

0

0

0

0

artfcl 4

0

1

-2

0

0

0

0

1

-1

0

0

0

0

0

0

0

0

artfcl 5

1

0

0

0

0

0

0

0

0

1

-1

0

0

0

0

0

0

artfcl 6

0

1

0

0

0

0

0

0

0

0

0

1

-1

0

0

0

0

artfcl 7

0

0

1

0

0

0

0

0

0

0

0

0

0

1

-1

0



 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Iteration ...