Julia is considering leasing a food booth outside Tech Stadium at home (6) football games.
If she clears $1000 in profit for each game she believes it will be worth leasing the booth.
$1000 per game to lease the booth
$600 to lease a warming oven She has $1500 to purchase food for first game and will for remaining 5 games
She will purchase her ingredients with money made from previous game.
Each pizza costs $6 for 8 slices which is $0.75 per slice, and she will sell it for $1.50
Each hot dog costs $0.45, and she will sell it for $1.50
Each BBQ Sandwich costs $0.90, and she will sell it for $2.25

Total revenue Total cost Profit
Pizza slice $1.50 $6/8 slices = $0.75 $0.75
Hot dog $1.50 $0.45 $1.05
Barbeque sandwich $2.25 $0.90 $1.35

x1 - number of pizza slices x2 - number of hot dogs x3 - number of barbeque sandwiches

The profit function: maximize Z = $0.75x1 + $1.05x2 + $1.35x3
There Z = total profit per game.

The oven size constraint is formulated as 16 shelves 3*4 feet each which will be filled twice for each game, so the maximum possible size of the stove is: (((12*3)*(12*4))*16)*2 = 55,296 square inches.

Estimate for each item in regards to the space:

Pizza slice 24.5 square inches ((14*14)/8)
Hot dog 16 square inches
Barbeque sandwich 25 square inches

1. Julia would increase her profit if she borrowed some more money from a friend. The shadow price, is $1.50 for each additional dollar that she earns. The upper limit given in the model is $1,658.88,