Julia' Food Booth

Assignment 3:

Julia’s Food Booth

Patrice Huff

Octavia Robertson

Shena Coleman

Tiffany Smith

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.

Variables:

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...