Abby Nathan is an MBA student at MSU, and she's investigating different ways to finance her graduate degree. She is considering leasing a food booth outside the Red Hawk Stadium at home football games. MSU sells out every home game, and Abby knows, from attending the games herself, that everyone eats a lot of food. She has to pay $1,000 per game for a booth, and the booths are not very large. Vendors can sell either food or drinks on MSU property, but not both. Only the MSU 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 Abby to prepare the food when she is selling it. She must prepare the food ahead of time and then store it in a warming oven. For $600 ($100 per game), 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 the half time.
Abby has negotiated with a local pizza delivery company to deliver 14-inch cheese pizzas 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 hotdog and $0.90 for each barbecue sandwich if she makes the barbecue herself the night before. She measured a hot dog and found it takes up about 16 square inches of space, whereas a barbecue sandwich takes up about 25 square inches. Since the 8-piece pie is 14 inches in diameter, she anticipates this will take up about 160 square inches.
She plans to sell a slice of pizza and a hot dog for $1.50 apiece and a barbecue sandwich for $2.25. Right now, 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.
Abby has talked to some students and vendors who have sold food at previous football games at MSU 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 barbecue sandwiches combined. She also anticipates that she will probably sell at least twice as many hotdogs as barbecue 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 Abby clears at least $1000 in profit for each game after paying all her expenses, she believes it will be worth leasing the booth.
QUESTIONS:
Formulate and solve a linear programming model for Abby that will help you advise her if she should lease the booth. HINT: Base the model on one single game. Solve model using solver - save Answer and Sensitivity reports.
If Abby were to borrow some more money from a friend before the first game to purchase ingredients, could she increase her profits? If so, how much should she borrow and how much additional profit would she make? HINT: Use the sensitivity report.
Abby found a new source for her BBQ sandwiches. They are slightly smaller and only take up about 22 square inches each and cost $0.80. However, given the reputation for her vendor, she can now sell them for $0.50 more each (i.e. $2.75). Re-run the LP to determine the optimal production mix and new profit.
Is your optimal production mix feasible? (Does it contain partial products (non-integer solutions)?) If so, re-run your problem again and require an integer solution. Did your production mix change significantly? Did you profit change significantly?
Abby is 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 Abby's analysis? Given these uncertainties and the results to questions 1 - 4, what do you recommend that Abby do?