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 $1,000 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 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 hot dog 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. She plans to sell a slice of pizza and a hot dog for $1.50 apiece and a barbecue 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 barbecue sandwiches combined. She also anticipates that she will probably 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 follows these general guidelines for demand. If Julia clears at least $1,000 in profit for each game after paying all her expenses, she believes it will be worth leasing the booth.
Case Problem “Julia’s Food Booth”
Complete the “Julia’s Food Booth” case problem on page 109 of the text. Address each of the issues A – D according the instructions given.
- (A) Formulate and solve an L.P. model for this case.
- (B) Evaluate the prospect of borrowing money before the first game.
- (C) Evaluate the prospect of paying a friend $100/game to assist.
- (D) Analyze the impact of uncertainties on the model.
The assignment will be graded using the associated rubric.
There are 12 points in each of the five criteria for a total of 60 points possible
|Criteria||0 Unacceptable (0 points)||1 Developing (6 points)||2 Competent (9 points)||3 Exemplary (12 points)|
|1. Formulate an LP model for this case. (Part A).||Did not submit or LP model is not sufficiently attempted and does not demonstrate a. recognizable attempt to model this case.||LP model is partially correct, but has errors in the objective function or constraints. Described with 70 – 79% accuracy, clarity, and completeness.||LP model has objective function and most constraints correctly specified. Described with 80 – 89% accuracy, clarity, and completeness.||LP model has objective function and all constraints fully and correctly specified. Described with 90 – 100% accuracy, clarity, and completeness.|
|2. Solve the linear programming model formulated in Criterion 1 (Part A)||Did not submit or did not solve the linear programming model accurately.||Solved the linear programming model with 70 – 79% accuracy.||Solved the linear programming model with 80 – 89% accuracy.||Solved the linear programming model with 90 – 100% accuracy.|
|3. Evaluate the prospect of borrowing money before the first game. (Part B).||Did not submit or did not evaluate accurately.||Evaluated and explained with 70 – 79% accuracy.||Evaluated and explained with 80 – 89% accuracy.||Evaluated and explained with 90 – 100% accuracy.|
|4. Evaluate the prospect of paying a friend $100/game to assist. (Part C)||Did not submit or did not evaluate accurately.||Evaluated and explained with 70 – 79% accuracy.||Evaluated and explained with 80 – 89% accuracy.||Evaluated and explained with 90 – 100% accuracy.|
|5. Analyze the impact of uncertainties in the model. (Part D)||Did not submit or did not analyze accurately.||Analyzed the impact with 70 – 79% accuracy, logic, and completeness.||Analyzed the impact with 80 – 89% accuracy, logic, and completeness.||Analyzed the impact with 90 – 100% accuracy, logic, and completeness.|