# Julias Food Booth

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Julias Food Booth A) Formulate and solve an L.P. model: Variables: x1 Pizza Slices x2 Hot Dogs x3 Barbeque Sandwiches Subject to:

Submitted by to the category Science and Technology on 03/01/2011 04:05 PM

Part A is also in the submitted QM solution

Maximize Total profit Z = \$0.75X1 + 1.05X2 +1.35X3

Constraints:

1. Budget constraint: 0.75X1+.45X2+.90X3=0

4. At least twice as many hot dogs as barbeque sandwiches

X2/X3>= 2.0

This constraint can be rewritten as:

X2-2X3>=0

X1, X2, X3 >= 0

Model: Maximize Total profit Z = \$0.75X1 + 1.05X2 +1.35X3

Subject to:

0.75X1+0.45X2+.90X3=0 (at least twice as many hot dogs as barbeque sandwiches)

X1= Pizza Slices

X2= Hot Dogs

X3= BBQ Sandwiches

Optimal Solution

X1= 1250, X2= 1250 X3= 0 Z= \$2,250.00

Julia should stock 1250 pizza slices, 1250 hot dogs and 0 BBQ sandwiches for a total profit of \$2,250.00

Booth cost= \$1000

Oven cost = \$100

After total expenses of \$1100.00, Julia would have a net profit of \$1150.00 meeting her requirement of a minimum of \$1000.00 profit. Julia should lease the booth for the season.

Part B

From the QM solution, Julia has used all of her available budget, there is no slack value indicating leftover funds. The solution also indicates that all the space in the oven has been used with no slack remaining. Julia would have no space for food so she should not borrow funds.

Part C

If Julia pays \$100.00 for help her cost increases accordingly and her profit drops to \$1050.00 Julia has still met her profit goal of \$1000.00

Part D

Weather, attendance, and food costs are all variables that could affect Julia’s profit. If sales aren’t as anticipated or the cost of doing business increases than the profit goal of \$1000 per game may not be met.

Given all the uncertainty and the fact that slight cost increases adversely affect profit, I would recommend that Julia not open the food booth.

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