# Julia's Food Booth Quantitative Methods 540

Quantitative Methods 540

Buddy L. Bruner, Ph.D.

Shirley Foster

11/25/2012

Assignment 3: Case problem “Julia’s Food Booth” Page 1 A. Julia Robertson is making an allowance for renting a food booth at her school. She is seeking ways to finance her last year and believed that a food booth outside her school’s stadium would be ideal. Her goal is to earn the most money possible thus increasing her earnings. In this case problem, she decided to sell pizza, hotdogs and BBQ sandwiches. The following LP model illustrates the maximum net profit and constraints that will determine whether or not to least the boot. Variables:

X1 – Pizza Slices

X2 – Hot Dogs

X3 – Barbeque Sandwiches

Subject to:

$0.75x1 + $0.45x2 + $0.90x3 ≤ $1,500

24x1 + 16x2 + 25x3 ≤ 55,296 in2 of oven space

X1 ≥ x2 + x3 (changed to –x1 + x2 + x3 ≤ 0 for constraint) X1, X2, X3 ≥ 0

Solution:

Variable | Status | Value |

X1 | Basic | 1250 |

Assignment 3 Case problem “Julia’s Food Booth” Page 2 X2 | Basic | 1250 |

X3 | NON Basic | 0 |

Slack 1 | NON Basic | 0 |

Slack 2 | Basic | 5296.0 |

Slack 3 | NON Basic | 0 |

Slack 4 | Basic | 1250 |

Optimal Value (Z) | | 2250 |

Built on the above LP model, Julia is estimated that she will earn a profit of $2,250.00. After paying for the rental lease, she has earned a net profit of $1,250.00. The model suggests that she rents the booth and sell only pizza and hotdog due to her spacing constraints. This is Julia best optimal results. B. Evaluate the prospect of borrowing money before the first game. In my opinion if Julia borrowed more money she could increase her profit. Any change in a coefficient in a parameter is carefully analyzed using sensitivity analysis. This analysis identifies any effect an independent variable might have on Julia’s given constraints, in this case her budget. The increase will generate an increase in product availability...

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