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Julia; S Food Booth

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Julia’s Food Booth
MAT 540
February 22, 2014

Julia’s Food Booth Case Problem (A) Formulate and solve an LP model.
Variables:
X1 = pizza slices, X2 = hot dogs, and X3 = barbeque sandwiches
Maximize Z = ($0.75 X1) + ($1.05 X2) + ($1.35 X3)
Subject to:
$0.75x1+ $0.45x2 + $0.90x3 ≤ $1,500
24x1 + 16x2 +25x3 ≤ 55.296in of oven space
X1 ≥ x2 + x3 (change to –x1 + x2 + x3 ≤ 0 for constraint)
X2/x3 ≥ 0
Solution:
X1 = 1250 pizza slices
X2 = 1250 hot dogs
X3 = 0 barbeque sandwiches
Z = $2,250 (B) Evaluate the prospect of borrowing money before the first game.
Yes, I do believe Julia would increase her profit if she borrowed money. The shadow price is $1.50 for each additional dollar she earns. The upper limit in the model that is given is $1,658.88. This means that Julia can borrow $158.88 from her friend, which gives her an extra profit of $238.32 or a total profit of $2,488.32. (C) Evaluate the prospect of paying a friend $100/game to assist.
According to the information presented in (A) and (B), I do believe Julia should hire her friend for $100 per game. It would be difficult for Julia to prepare all of the food needed within the amount of time to reach her goal, so she will need the additional help. If she is borrowing extra money from another friend, she would be able to pay the help for the time spent helping at the game because the $158.88 she borrowed will allow her to do so. (D) Analyze the impact of uncertainties on the model.
An impact of uncertainty on the model would be that the weather could cause people to not attend the game. If the weather is rainy, then many people may not attend as they would if it was sunny. All together what if the game is cancelled because of weather? With this being an issue, Julia may not reach her goal of $1000 per game. In addition to the weather, the pizza company Julia negotiated the deal with

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