Julia's Food Booth

Julia's Food Booth

Case Study

MATH 540, Quantitative Methods

Julia is a senior at Tech University and wants to find a way to make extra money to finance her final year at school. She is considering leasing a food booth outside the Tech stadium during home football games. Julia knows the games sell out and the crowd eats a lot of food. Julia will look at the following items to determine if it is a good decision. The first item is creating an L.P. model to help understand the constraints and how to maximize her profit.

Julia wants to sell Pizza, Hot Dogs, and Bar-B-Q sandwiches. Julia is going to have a Pizza company deliver a 14 inch Pizza twice each game which will cost her $6.00, Julia estimates it will cost her $0.45 per Hot Dog, and $0.90 for each Bar-B-Q sandwich. Julia plans to sell a slice of Pizza and a Hot Dog for a $1.50 a piece and a sandwich for $2.50. Julia also has to lease a warming oven for the food items for $600, this warming oven has 16 shelves and measure 3x4 each. Julia has $1500.00 in cash to purchase the food ingredients for the first game and $1000 to lease her booth and Julia would like to clear at least $1000.00 profit each game. By looking at the L.P. model she can determine if she should lease the booth.

(Note: The oven space needed for a slice of pizza is determined by dividing the total space required by the slice of pizza, 14 x 14 = 196 inch by 8 or 24 in2 per slice. The total space available would be the dimensions of the shelf, 36 in. x 48 in. = 1,728 inch, multiply that by 2, the times before kickoff and halftime, thus the oven will be filled 55,296 inch).

A) Formulate and solve an L.P. model for this case:

X1 = number of pizza slices

X2 = number of hot dogs

X3 = number of BBQ sandwiches

This model is set up for the first home game.

Maximize, Z = $0.75 x1 + 1.05 x2 + 1.35 x3 which is subject to the following:

$0.75 x1 + 0.45 x2 + 0.90 x3 <= 1500 C1

24 x1 + 16 x2 + 25 x3 <= 55296...