# Assignment # 3 Math 540

**Topics:**English-language films, Rain, American films

**Pages:**2 (467 words)

**Published:**September 16, 2012

Case Problem "Julia's Food Booth"

Jenna Kiragis

Strayer University

8/24/2012

Assignment #3: Case Problem "Julia's Food Booth" Page 2 A) Formulate and solve an L.P. model:

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) x2/x3 ? 2 (changed to –x2 +2x3 ? 0 for constraint)

x1, x2, x3 ? 0

Solution:

Variable | Status | Value |

X1 | Basic | 1250 |

X2 | Basic | 1250 |

X3 | NONBasic | 0 |

slack 1 | NONBasic | 0 |

slack 2 | Basic | 5296.0 |

slack 3 | NONBasic | 0 |

slack 4 | Basic | 1250 |

Optimal Value (Z) | | 2250 |

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

B) Evaluate the prospect of borrowing money before the first game.

Yes, Julia would increase her profit if she borrowed some more money from a friend. The shadow price, or dual value, is $1.50 for each additional dollar that she earns. The upper limit given in the model is $1,658.88, which means that Julia can only borrow $158.88 from her friend, giving her an additional profit of $238.32. Based on the sensitivity analysis, the upper limit of the sensitivity range for budget is $158.00 allowing her to have a maximum budget of $1658.00. Her shadow price reflects an increase of $1.50 for any additional resource. Therefore if she borrows the maximum of $158.88, she will yield an increase in profit of $238.32 and total profit of $2,488.32.

C) Prospect of paying a friend $100/game to assist

Yes, I believe Julia should hire her friend for $100 per game. In order for Julia to prepare the hot dogs and barbeque sandwiches needed in a short period of time to make her profit, she needs the additional help. Also, with...

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