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

Mat540

Quantitative Methods

August 22, 2012

Julia’s Food Booth

(A) Formulate and solve a L.P. model for this case. Variables:

Pizza - X1 $1.33 $1.50 14 inches

Hot Dogs - X2 $0.45 $1.50 16 square inches

Barbecue - X3 $0.90 $2.25 25 square inches

Maximize Z= $0.75x1, 1.05x2, 1.35x3 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: x1 = 1,250 pizza slices x2= 1,250 hot dogs x3= 0 barbecue sandwiches Z= $2,250 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 |

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

Yes, Julia would increase her profit if she borrowed money from a friend before the first game to purchase more ingredients. Her outcome would be an increase in profit. 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 simply means that Julia can only borrow $158.88 from her friend, giving her an additional profit of $238.32.

C) Evaluate the prospect of paying a friend $100/game to assist.

I believe Julia should hire her friend for $100 per game. Julia needs the additional help in order to prepare the hot dogs and barbeque sandwiches needed in a short period of time to make her profit. Also, when borrowing the extra $158.88 from her friend, Julia will be able to pay her friend for the time spent per game for helping with the food booth based on her profit.

D) Analyze the