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Julia’s Food Booth
J. Olivia Prince-Griffith
February 23, 2012
MAT 540: Quantitative Methods
Dr. Donald Demoulin
(A) Formulate and solve an L.P. model for this case.
x1: Pizza Slices
x2: Hot Dogs
x3: Barbeque Sandwiches
$0.75x1 + $0.45x2 + $0.90x3 < $1,500
24x1 + 16x2 + 25x3 < 55,296 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
Variable: Status: Value
X1: Basic: 1250
X2: Basic: 1250
X3: Nonbasic: 0
Slack 1: Nonbasic: 0
Slack 2: Basic: 5296
Slack 3: Nonbasic: 0
Slack 4: Basic: 1250
Optimal Value (z): 2250
(B) Evaluate the prospect of borrowing money before the first game.
I would agree that Julia should borrow money from her friend to increase her profit. The dual value, also known as shadow price, is $1.50 for each additional dollar that is earned. $1,658.88 is the upper limit given, which means that the amount that Julia should borrow from her friend is $158.88. By her borrowing this amount, it will give her an additional profit of $238.32
(C) Evaluate the prospect of paying a friend $100/game to assist.
Julia should hire her friend at $100 per game. The additional help will be needed in order for Julia to be able to prepare the barbeques sandwiches and hot dogs in a short period time to earn profit. With the $158.88 borrowing from the friend, she will be able to pay her friend the $100 per game for the help she will be providing.
(D) Analyze the impact of uncertainties on the model.
Weather will be a major uncertainty that plays a factor in Julia’s analysis. Due to the weather unpredictable changes, it is hard to determine the amount of profit that can be earned. The crowd can be determined by the type of weather it is. For example, the crowd want be as large if it is...
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