Assignment #3

The following variables will be used:

X1 = Slices of PizzaX2 = Hot DogsX3 = BBQ Sandwiches

The objective is to maximize profit.maximize Z= 0 .75X1+1.05X2+1.35X3

Subject to:0.75X1+1.05X2+1.35X31,500(Budget)

24X1+16X2+25X355,296in2 (Oven space)

X1X2+X3

X2X32.0

X1, X2, X30

Julias Food Booth

Food items:PizzaHot DogsBarbecue

Profit per item:0.751.051.35

Constraints:AvailableUsageLeft over

Budget ($)0.750.450.90 1,500 1,500.00 0

Oven space (sq. in.)241625 55,296 50,000.00 5296

Demand1-1-10 - 0

Demand

0

1

-2

0

1,250.00 -1250

Stock

Pizza=1250slices

Hot Dogs=1250hot dogs

Barbecue=0sandwiches

Profit=2,250.00

Sensitivity ReportAdjustable Cells

FinalReducedObjectiveAllowableAllowable

CellNameValueCostCoefficientIncreaseDecrease

$B$12Pizza=125000.7511.00

$B$13Hot Dogs=125001.051E+300.27

$B$14Barbecue=001.350.3750000111E+30

Constraints

FinalShadowConstraintAllowableAllowable

CellNameValuePriceR.H. SideIncreaseDecrease

$G$9Demand Usage1,250.00 - 012501E+30

$G$7Oven space (sq. in.) Usage50,000.00 - 552961E+305296

$G$6Budget ($) Usage1,500.00 1.50 1500158.881500

$G$8Demand Usage - (0.38)020003333.33

I believe that Julia would increase her profit if she borrowed some more money from a friend. Her shadow price, or dual value, is $1.50 for each additional dollar that she earns. The upper limit given in the model is $1,658.88, which means that Julia can borrow only $158.88 from her friend, which would give her an additional profit of $238.32. Evaluate the prospect of paying a friend $100/game to assist.In order for Julia to be able to prepare the BBQ sandwiches and hot dogs in a short period of time to make her profit, she needs the additional help. With her borrowing the extra $158.88 from her friend, Julia would be able to pay her friend for the time that is spent per game helping with the food booth.

Analyze the impact of uncertainties on the model.I think that the biggest uncertainty in this model is the demand. While Julia may have a good idea of what people will buy and not buy during the game, the demand can shift from game to game and it is not always constant. Consequently, if the demand changes then the solution to the linear programming will change, and it could affect her ability to make a profit greater than $1000. I think the weather plays an important role in food booth sales. For example the weather may be too hot for hotdogs and pizza. It also may be too cold for food and the people would rather have hot chocolate or coffee. The weather could also affect how many fans are willing to attend the games in general. For this reason I feel that the weather would have the greatest affect on food sales and it would determine Julias overall success or failure. I would recommend adjusting the food items she sells based on the weather conditions (such as hot chocolate) to offset the losses based on historical data that is affected by weather.