Case Problem” Julia’s Food Booth”

Julia’s objective is to maximize total profit; the total profit is the summary of the individual profits gained from each pizza slice, hot dog, and barbeque sandwich.

I am going to estimate the profit for each item as difference between total revenue and total cost of the item. 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 = $0.75* x1 + $1.05 * x2 + $1.35 * x3
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 (14*14)/8 = 24.5 square inches (keeping in mind that she will keep whole pizza warm)
Hot dog 16 square inches
Barbeque sandwich 25 square inches

The budget size constraint is formulated as $1,500 cash available for purchase of product components and preparing the food items for the first game.

In this example there are fractional relationships between variables:
- Julia can expect to sell at least as many slices of pizza as hot dogs and barbeque