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What are the differences between deterministic and probabilistic techniques?
A group of friends are planning a recreational outing and have constructed the
following payoff table to help them decide which activity to engage in. Assume that the
payoffs represent their level of enjoyment for each activity under the various weather
conditions.
Weather
Cold Warm Rainy
S1 S2 S3
Bike: A1 10 8 6
Hike: A2 14 15 2
Fish: A3 7 8 9
If the group is optimistic, what decision should they make?
Saba conducts regular tours of his favorite city in the world, Paris. Each semester he
selects among the finest students in the university and escorts them to the City of
Lights. In addition to a world-class education on conducting business in Europe, he
arranges a number of cultural outings for them to help them immerse themselves in all
that France has to offer. He collects an extra $100 from each student for this purpose
and limits his tour group to ten lucky individuals. Some of the events (and their prices)
he proposes to the students include:
Eiffel Tower visit, $40 per student, E
Paris Sewer spelunking, $20 per student, S
Half day passes to the Louvre, $60 per student, L
Bon Beret tour, $50 per student, B
So much to do and so little time!
What would the constraints be if the Eiffel Tower visit needed to take place at the same
time as the half day at the Louvre and if students taking the Paris Sewer tour had to
wear the special sanitary beret available only from the Bon Beret tour?
The fact that the first toss of a coin has no effect on the outcome of the second toss of
the coin suggests that these events are ________.
In the basic EOQ model, if D = 80 per month, Co = $13, and Cc = $11 per unit per
month, what is the EOQ?
For the following transition matrices, determine the transient or absorbing states.
Given the following linear programming problem:
maximize Z = $100x1 + 80x2
subject to x1 + 2x2 ≤ 40
3x1 + x2 ≤ 60
x1, x2 ≥ 0
Using the simplex method, what is the optimal value for X2?
The Cruise
Their cruise would port out of New Orleans and promised seven days with a panoply of
excursions in Jamaica, Cozumel, and Grand Cayman. A list of excursions at each site
and key features of each appear in the table. The excursions were all day affairs, so it
was possible to engage in only one per port. The cruise ship sailed at night and docked
at each of these three ports at the crack of dawn. By dinner time, the ship was on its
way to the next port and next set of excursions. The couple was energetic and active for
a pair of 52 year-olds., and while enjoying an upper middle class lifestyle, they didn't
want to spend money on excursions that might be better spent on tacky souvenirs. The
couple therefore budgeted $250 for the excursions the prices shown are per couple, so
for example, the $60 will pay for both of them to fill up on jerk chicken and mannish
water.
For each of the duplicate excursions (e.g., snorkeling is offered in all three ports), the
couple researched the quality of the activity and ranked the excursion among the
available alternatives, with higher numbers indicating better quality. Thus, snorkeling in
Jamaica is better than in Cozumel, and snorkeling in Cozumel is better than in Grand
Cayman. For the unique experiences, i.e., the turtle farm, the default rating was the a 3.
(Note - data used in this test question should not be construed as vacation advice.)
What is an appropriate objective function for this vacation?
An investor is consider four different opportunities, A, B, C, or D. The payoff for each
opportunity will depend on the economic conditions, represented in the payoff table
below.
Economic ConditionPoor Average Good ExcellentInvestment (S1) (S2) (S3) (S4)
A 50 75 20 30
B 80 15 40 50
C -100 300 -50 10
D 25 25 25 25
If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 05, respectively,
what investment would be made using the expected value criterion?
Canning Transport wants to move goods from three (3) factories to three (3) distribution
centers. Information about the move is given below:
Shipping costs are (in $):
According to the Vogel's Approximation Method, the initial solution would have a total
transportation cost of ________.
In using the simplex method, ________ optimal solutions are identified by cj - zj = 0 for
a non-basic variable.
The Vacation
Final exams are almost here and once they are done, it will be time to reward myself
with a well-deserved vacation. As a state employee, I haven't seen a raise since... well,
ever. Thus an important criterion, in fact the most important criterion is to find an exotic
region that can be visited inexpensively. There are three states of nature that could
impact costs in these five areas of interest, and they correspond to the relative strength
of the US Dollar against that region's dominant currency. Rather than squander my time
doing any actual publishable research, instead I have determined the average cost per
day to visit each region under each of the possible states of nature. This table, which
should not be construed as actual vacation advice, appears below.
My wife always looks on the bright side of life. Where would she recommend we travel
and why?
Given an EOQ model with shortages in which annual demand is 4200 units, Co = $160,
Cc = $7 per unit per year and CS = $25, what is the optimal stock out level?
Lenny, a graduate research assistant "moonlights" at the short order counter in the
student union snack bar in the evenings. He is the only one on duty at the counter
during the hours he works. Arrivals to the counter seem to follow the Poisson
distribution with a mean of 8 per hour. Each customer is served one at a time and the
service time follows an exponential distribution with a mean of 5 minutes.
On average, how many people are either waiting in line or currently being served?
If the number of unique assignments is less than the number of rows, then a ________
test must be used.
A strategy is ________ and can be eliminated if all its payoffs are worse than the
corresponding payoffs for another strategy.
The linear programming problem whose output follows determines how many red nail
polishes, blue nail polishes, green nail polishes, and pink nail polishes a beauty salon
should stock. The objective function measures profit; it is assumed that every piece
stocked will be sold. Constraint 1 measures display space in units, constraint 2
measures time to set up the display in minutes. Constraints 3 and 4 are marketing
restrictions.
MAX 100x1 + 120x2 + 150x3 + 125x4
Subject to 1. x1 + 2x2 + 2x3 + 2x4 ≤ 108
2. 3x1 + 5x2 + x4 ≤ 120
3. x1 + x3 ≤ 25
4. x2 + x3 + x4 > 50
x1, x2, x3,x4 ≤ 0
Optimal Solution:
Objective Function Value = 7475.000
Objective Coefficient Ranges
Right Hand Side Ranges
To what value can the profit on red nail polish drop before the solution would change?
Robert wants to know if there is a relation between money spent on gambling and
winnings.
What is the coefficient of determination?
