Case Problem “Julia’s Food Booth”

Case PROBLEMS 109
evenings they could have a staff reduction of as much as However, Zooey has noted that Pierre has already made
5 hours. How would this affect their profit level? plans based on the number of dinners recommended by
C. The final question they would like to explore is raising the the linear programming solution. Angela has suggested a
price of the fish dinner. Angela believes the price for a fish price increase that will increase profit for the fish dinner to
dinner is a little low and that it could be closer to the price $14. Would this be acceptable to Pierre, and how much
of a beef dinner without affecting customer demand. additional profit would be realized?
Case Problem
ULIAlS FOOD BOOTH remaining five games she will purchase her ingredients with
money she has made from the previous game.
Iulia has talked to some students and vendors who have sold
ulia Robertson is a senior at Tech, and she’s investigating differ- feed 3‘ P1‘eVie’U5 feet-he]-l Semee at Teeh 35 Well 35 at Other 11hh*’e”‘
lent ways to finance her fine; Year at eel-,ee1_ she is eeneideeing sities. From this she has discovered that she can expect to sell at
leasing a food booth outside the Tech stadium at home football leeet 33 mehl’ Slices ‘of Pheze 35 hell C1035 ehd herheehe eehdwlehee
games. Tech sells out every home game, and Julia knows, from combined. She also anticipates that she will probably sell at least
attending the games herself, that everyone eats e 10; of fe,e,d_ she twice as many hot dogs as barbecue sandwiches. She believes that
has te, pay $1,000 per game for a booth, and the booths are not she will sell everything she can stock and develop a customer base
ee_.n,1arge_ Vendors e-an Sen either food or drinks on Teeh proper- for the season if she follows these general guidelines for demand.
ty, but not both. Only the Tech athletic department concession If lhhe eleere at leeet 31:00″ ih Profit fer eeeh game after P3?‘
stands can sell both inside the stadium. She thinks slices of cheese ihg 3“ her exPeh5e5» She hehe”~’e5 it will he Wefth leeeihg ‘he he°th+
pizza, hot dogs, and barbecue sandwiches are the most popular A. Formulate and solve a linear programming model for Julia
food items among fans and so these are the items she would sell. that will help you advise her if she should lease the booth.
Most food items are sold during the hour before the game B. If Iulia were to borrow some more money from a friend
starts and during half time; thus it will not be possible for Julia to before the first game to purchase more ingredients, could
prepare the food while she is selling it. She must prepare the food she increase her profit? If so, how much should she borrow
ahead of time and then store it in a warming oven. For $600 she and how much additional profit would she make? What
can lease a warming oven for the six-game home season. The oven factor constrains her from borrowing even more money
has 16 shelves, and each shelf is 3 feet by 4 feet. She plans to fill the than this amount (indicated in your answer to the previous
oven with the three food items before the game and then again question)?
before half time. C. When Iulia looked at the solution in (A), she realized that it
Iulia has negotiated with a local pizza delivery company to would be physically difficult for her to prepare all the hot
deliver 14-inch cheese pizzas twice each game-2 hours before the dogs and barbecue sandwiches indicated in this solution._
game and right after the opening kickoff. Each pizza will cost her She believes she can hire a friend of hers to help her for $100
$6 and will include 8 slices. She estimates it will cost her $0.45 for per game. Based on the results in (A) and (B). is this some-
each hot dog and $0.90 for each barbecue sandwich if she makes thing you think she could reasonably do and should do?
the barbecue herself the night before. She measured a hot dog and D. Iulia seems to be basing her analysis on the assumption that
found it takes up about 16 square inches of space, whereas a bar- everything will go as she plans. What are some of the
becue sandwich takes up about 25 square inches. She plans to sell uncertain factors in the model that could go wrong and
a slice of pizza and a hot dog for $1.50 apiece and a barbecue adversely affect ]ulia’s analysis? Given these uncertainties
sandwich for $2.25. She has $1,500 in cash available to purchase and the results in (A), (B), and (C), what do you recom-
and prepare the food items for the first home game; for the mend that Julia do?
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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.

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