Julia Robertson is a senior at Tech, and she's investigating different ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game, and Julia knows, from attending the games herself, that everyone eats a lot of food. She has to pay $1000 per game for a booth, and the booths are not very large. Vendors can sell either food or drinks on Tech property, but not both. Only the Tech athletic department concession stands can sell both inside the stadium. She thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans and so these are the items she would sell.

Most food items are sold during the hour before the game starts and during half time; thus it will not be possible for Julia to prepare the food while she is selling it. She must prepare the food ahead of time and then store it in a warming oven. For $600 she can lease a warming oven for the six game home season. The oven has 16 shelves, and each shelf is 3 feet by 4 feet. She plans to fill the oven with the three food items before the game and then again before half time.

Julia has negotiated with a local pizza delivery company to deliver 14 inch cheese pizza twice each game-2 hours before the game and right after the opening kickoff. Each pizza will cost her $6 and will include 8 slices. She estimates it will cost her $0.45 for each hot dog and $0.90 for each barbeque sandwich if she makes the barbeque herself the night before. She measured a hot dog and found it takes up about 16 square inches of space, whereas a barbeque sandwich takes up about 25 square inches. She plans to sell a slice of pizza and a hot dog for $1.50 apiece and a barbeque sandwich for $2.25. She has $1,500 in cash available to purchase and prepare the food items for the first home game; for the remaining five games she will purchase her ingredients with money she has made from the previous game.

Julia has talked to some students and vendors who have sold food at previous football games at Tech as well as at other universities. From this she has discovered that she can expect to sell at least as many slices of pizza as hot dogs and barbeque sandwiches combined. She has anticipated that she will probably sell at least twice as many hot dogs as barbeque sandwiches. She believes that she will sell everything she can stock and develop a customer base for the season if she follows these general guidelines for demand.

If Julia clears at least $1000 in profit for each game after paying all her expenses, she believes it will be worth leasing the booth.

A. Formulate and solve a linear programming model for Julia that will help you advise her if she should lease the booth.

B. If Julia were to borrow some more money from a friend before the first game to purchase more ingredients, could she increase her profit? If so, how much should she borrow and how much additional profit would she make? What factors constrains her from borrowing even more money that this amount (indicated in your answer to the previous question)?

C. When Julia looked at the solution in (A), she realized that it would be physically difficult for her to prepare all the hot dogs and barbeque sandwiches indicated in this solution. She believes she can hire a friend of hers to help her for $100 per game. Based on the results in (A) and (B), is this something you think she could reasonably do and should do?

D. Julia seems to be basing her analysis on the assumption that everything will go as she plans. What are some of the uncertain factors in the model that could go wrong and adversely affect Julia's analysis? Given these uncertainties and the results in (A), (B), and (C), what do you recommend that Julia do?

ADDENDUM

After graduating from Tech Julia was unable to find regular employment and approached the Director of Athletics at Tech to request that she remain a vendor of the following year. The Director was so impressed by Julia's progress and professionalism from the year before he decided to allow her to continue to be a vendor for the next season with the following conditions and changes:

a. Julia must do an 80:20 split of all of her profits with the Department of Athletics. Julia also has the ability to sell soft drinks. If she decides to sell soft drinks, she must agree to a 50:50 split; however, the department will not provide any monetary funding. Julia's cost for the soft drinks are 55 cents, and she sells them for two dollars. She can expect to sell just as many soft drinks as all food items combined.

b. Julia must sell food from two (2) booths; however, she will pay the same price as she paid for one booth during the previous season.

c. The department of athletics is able to use the warming ovens owned by food services at no cost since all student athletes on scholarship have a meal plan. There are three (3) warming ovens available to Julia. The warming ovens are the same capacity as those used the previous season.

d. Julia has the same options available for the types of food to sell however, she is able to take advantage of a discount that the school receives from the same vendor she purchased the pizza, hot dogs and sandwiches from; the discount is 18%, 23% and 42% respectively.

e. Due to the operation of two (2) booths, Julia must hire at least two additional persons.

After paying off here loans from the previous season, she has $2750.00 in savings from a part-time job at the mall, which she is able to invest in the venture. If Julia clears at least $2500.00 in profit for each game after paying all her expenses, she believes it will be worth the partnership with the Department of Athletics.

Formulate and solve a linear programming model for Julia that will help you advise her on which offer to accept from the director if any. Julia's younger brother who is a freshman at Tech wants to help Julia increase her profits by loaning her some money using his school refund check. Her brother's only requirement is that she repays him by the end of the season and he is allowed to get into the games free by posing as one of her assistants and receiving free food for him and his girlfriend. If Julia decides to take him up on his offer, how much should she borrow, if anything?

What is your recommendation to Julia?