# Mat 540 - Assignment 3

### Mat 540 - Assignment 3

Assignment 3: Julia’s Food BoothQuantitative Methods - MAT

Assignment #3: Julia’s Food Booth

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

X1 = pizza slices

X2 = hot dogs

X3 = B B Q sandwiches

This model is set up for the first home game.

Next, you would maximize Z = $0.75 x1 + 1.05 x2 + 1.35 x3 which is subject to the following:

$0.75x1 + 0.45x2 + 0.90x3 = 2.0 so x1, x2, x3 >=0

X3

All of which is displayed in the graph below. (Note: The oven space needed for a slice of pizza is determined by dividing the total space required by the slice of pizza, 14 x 14 = 196 in^2 by 8 or 24 in^2 per slice. The total space available would be the dimensions of the shelf, 36 in. x 48 in. = 1,728 in^2, multiply that by 2, the times before kickoff and halftime, thus the oven will be filled 55,296in^2.

Solution: X1 = 1,250 slices of pizza

X2 = 1,250 hot dogs

X3 = 0 bbq sandwiches

Z = $2,250

| | | | | | | | |

Food items: | | Pizza | Hot Dogs | Barbecue | | | | |

Profit per item: | 0.75 | 1.05 | 1.35 | | | | |

Constraints: | | | | Available | Usage | Left over | |

Budget ($) | 0.75 | 0.45 | 0.90 | 1,500 | 1,500.00 | 0 | |

Oven space (sq. in.) | 24 | 16 | 25 | 55,296 | 50,000.00 | 5296 | |

Demand | 1 | -1 | -1 | 0 | - | 0 | |

Demand | 0 | 1 | -2 | 0 | 1,250.00 | -1250 | |

| | | | | | | | |

Stock | | | | | | | | |

Pizza= | 1250 | slices | | | | | | |

Hot Dogs= | 1250 | hot dogs | | | | | | |

Barbecue= | 0 | sandwiches | | | | | | |

Profit= | 2,250.00 | | | | | | | |

Julia’s profit before expenses should be $2,250. The lease is $1,000 per game thus giving a profit of $1,250.00. Then she had the cost of leasing the warming oven of $100, leaving her with $1150, thus making it worth her while to lease the booth.

Another aspect to look at is the $1,500...