Julia's Food Booth

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Julia’s Food Booth

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|

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.

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 her borrowing the extra $158.88 from her friend, Julia would be able to pay her friend for the time spent per game helping with the food booth.

D) Analyze the impact of uncertainties on the model
A major uncertainty that could play a factor in Julia’s analysis in weather. Weather is always un predictable and it could be sunny one day and raining the next. If the weather is rainy, there may not be as big of a crowd as there is on a nice day. The weather might also be too cold or too hot and game patrons may not want to eat before and during half time. Julia has to reach her goal of at least $1,000 per game so that she can pay for the booth each home...
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