# Julia’s Food Booth Case Problem

MAT 540- Quantitative Methods

February 23, 2013

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

The following variables were be used:

X1 = Slices of Pizza

X2 = Hot Dogs

X3 = BBQ Sandwiches

The objective is to maximize profit.

maximize Z= 0 .75X1+1.05X2+1.35X3

Subject to:

0.75X1+1.05X2+1.35X3≤1,500 (Budget)

24X1+16X2+25X3≤55,296in2 (Oven Space)

X1≥X2+X3

X2X3≥2.0

X1, X2, X3≥0

(B) Evaluate the prospect of borrowing money before the first game. Following table shows the sensitivity report from excel solver | | | | | | |

| | | | | | | | |

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 | | | | | | | |

| | | | | | | | |

| | | | | | | |

Adjustable Cells| | | | | |

| | | Final| Reduced| Objective| Allowable| Allowable| | Cell| Name| Value| Cost| Coefficient| Increase| Decrease| | $B$12| Pizza=| 1250| 0| 0.75| 1| 1.00|

| $B$13| Hot Dogs=| 1250| 0| 1.05| 1E+30| 0.27|

| $B$14| Barbecue=| 0| 0| 1.35| 0.375000011| 1E+30| | | | | | | | |

Constraints| | | | | |

| | | Final| Shadow| Constraint| Allowable| Allowable| | Cell| Name| Value| Price| R.H. Side| Increase| Decrease| | $G$9| Demand Usage| 1,250.00 | - | 0| 1250| 1E+30| | $G$7| Oven...

References: Taylor, B. M. (2010). Introduction to management science (11th ed.). Upper Saddle River, NJ: Pearson/Prentice Hall.

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