Asu Vakharia is a senior at Tech and shes investigating different ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium home football games. Tech sells out every home game, and Asu knows from attending the games herself that every- one eats a lot of food. She has to pay $300 per game for a booth, and the booths are not very large. Ven- dors can either sell 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, 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 Asu 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 $1200 she can lease a warming oven for the six-game home sea- son. The oven has 10 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 be- fore half-time. Asu has negotiated with a local pizza delivery company to deliver 16-inch cheese pizzas twice each game two hours before the game and right after the Assignment opening kickoff. Each pizza will cost her $18.00 and will include 8 slices. She estimates it will cost her $1.00 for each hot dog and $2.00 for each barbecue sandwich if she makes the barbecue herself the night before. She measured a hot dog and found it takes up about 14 in2 of space, whereas a barbecue sand- wich takes up about 16 in2. She plans to sell pizza for $3.00 per slice, hot dogs for $1.50 each, and bar- becue sandwiches for $2.50 each. She has $2,000 in cash available to purchase items for the first home game; for the remaining five games she will purchase her ingredients with money she has made from the previous games. (Assume that Asu can pay for the first games booth rental after the game.) Asu 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 discov- ered that she can expect to sell at least as many slices of pizza as hot dogs and barbecue sandwiches com- bined. She also anticipates that she will sell at least twice as many hot dogs as barbecue sandwiches. She believes that she will sell everything she can stock and develop a customer base for the season if she fol- lows these general guidelines for demand. If Asu clears at least $800 in profit for each game after paying all of her expenses she believes it will be worth leasing the booth.

Case Questions

1. Formulate and solve a linear optimization model for Asu that will help you advise her if she should lease the booth. (Assume that Asu can pay for the first games booth rental after the game.) [4.0 pts]

Be sure to define the decision variables explicitly and to write out the objective function and con- straints clearly.

Identify at least two key assumptions that you have made in order to formulate and solve this problem.

In addition to the mathematical expressions, provide a brief explanation of the formulation in words.

2. If Asu were to borrow some more money from a friend before the first home 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 factor constrains her from borrowing even more money than this amount (i.e., the amount indicated in your answer to the previous question)? [1.5 pts]

3. When Asu looked at the solution to Question 1, she realized that it would be physically difficult for her to prepare all the hot dogs and barbecue 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 Questions 1 and 2, is this something you think she could reasonably do and should do? [1.5 pts]

4. Asu 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 Asus analysis? Given these uncertainties and the results in Questions 1, 2, and 3, what do you recommend that Asu do? [1.5 pts]