I need help solving the first problem and formulate linear programming.
BUAD 311 ??? Spring 2016
Homework #2 Optimization and Revenue Management (Update: March 21)
Due Wednesday, March 30
Students can discuss homework questions with each other or with the TA/instructor, provided that the
actual work is done individually. Homework assignments are accepted only via Blackboard, and I expect
most students to use Word (You do not need to submit your excel file that includes your LP formulation
and solver solution for Q1). Please show your work. You may not receive a full credit if you just provide
an answer without showing any work.
Q1 (30 points) In this question, your task is to demonstrate that we can use the LP technique to
As you can see in the above figure, we are sending oil from the field to the refinery. There are many
pumping stations between the oil field and the refinery, but for the purpose of this homework, we
consider only two pumping stations. The oil field, pumping stations, and the refinery are connected with
pipes. Oil can go only one way. For example, oil can flow from F to A and A to B, but not R to A. Each
pipe has a capacity. For instance, the pipe that connects the oil field and the pumping station A has a
capacity of 700 barrels/day.
a) (13 points) Formulate an LP to find the capacity of the system.
b) (3 points) Enter your formulation to Excel and use Solver. What is the capacity of the system in
c) (3 points) Using the answer report, calculate the new daily capacity of the system when the
capacity of the pipe from the Oil Field to Station B is increased to 700 barrel/day.
d) (7 points) Now suppose our goal is to send 700 barrels a day from Oil Field to the Refinery (note
that this may be less than the capacity in part b, also ignore part c). The cost of using Station A is
$2 per barrel. For Station B is $3 per barrel. Formulate an LP to minimize the cost.
e) (2 points) Now enter your formulation from part d) to Excel and use Solver. What is the cost of
sending 700 barrels from Oil Field to the Refinery?
f) (2 points) Using the sensitivity analysis report, calculate the new daily cost of the system if the
cost of using Station B is reduced to $2.5 per?barrel. Note that it is possible that your
formulation may not allow to use sensitivity analysis to answer this question. If that?s the case,
go back to part d and revise your formulation.
Q2 (24 points) Trojan Resort is an exclusive resort on a private island with 4 ocean front cabins. There
are two types of customers: leisure travelers and jet setters. Leisure travelers always book their cabins
at least two weeks before their intended stays, and pay $500 per night. Jet setters tend to reserve their
cabins late, just a few days before their arrivals, and pay $2,000 per night. The durations of stay for both
leisure travelers and jet setters are the same. To simplify the calculation, assume that both leisure
travelers and jet setters only stay for one night. The distribution of the number of jet setters is given in
the following table:
Number of Jet Setters
0.3 0.5 0.2
a) Determine the number of cabins that Trojan Resort should reserve for the jet setters in order to
maximize its total expected revenue.
b) Not only the management team wants to know the optimal number of cabins to reserve for jet
setters, but they also want to figure out what is the expected revenue if 1, 2, or 3 cabins are
reserved. Calculated the expected revenue for the three cases (assuming sufficient leisure
c) Suppose the number of leisure travelers is between 1 (inclusive) and 4 (inclusive), with all
numbers being equally likely. Furthermore, Trojan Resort decides to reserve 2 cabins for the jet
setters. Determine the total expected revenue for Trojan Resort. (Hint: you may want to draw a
decision tree and use your answers from part b)
d) Hoping to increase its revenue, Trojan Resort is running an advertising campaign that will attract
more leisure travelers to its property. With the ad campaign, the management estimates that
the number of leisure travelers will be uniformly distributed between 4 (inclusive) and 8
(inclusive). The campaign will not affect the number of jet setters coming to the resort. Given
the anticipated increase in the leisure travelers, how many cabins should Trojan Resort reserve
for the jet setters? How much additional profit is generated through the campaign?
Q3 (16 points) Vertigo Air is considering adding a new flight from LAX to Bratislava for the next year.
Vertigo Air has the option of either operating this flight in the same time slot as its competing airline
Giddy Air, or to choose a different time. Further, it believes the response to the flight will be favorable,
neutral, or unfavorable with probabilities 0.3, 0.4, and 0.3 respectively. However, Vertigo Air may invest
heavily in advertising and increase the probability of a favorable response to 0.5 while lowering the
probabilities of neutral and unfavorable responses to 0.3 and 0.2, respectively. Advertising costs $10
Million. The table below details the revenues generated by operating the flight:
Revenue ($ Million)
Same Slot as Giddy Air
a) (12 points) Draw the decision tree for Vertigo Air.
b) (4 points) Should Vertigo invest in advertising or not? Should Vertigo choose the same time slot
or a different time slot?
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