MAT 540 Quantitative Methods

MAT
540 Quantitative Methods
1.In an unbalanced transportation model, supply does not equal
demand and one set of constraints uses ? signs.
2. In a transshipment problem, items
may be transported from destination to destination and from source to source.
3.Adjusted exponential smoothing is an exponential smoothing
forecast adjusted for seasonality.
4. A cycle is an up and down
movement in demand that repeats itself in less than 1 year.
5. If we are solving a 0-1 integer
programming problem, the constraint x1 = x2 is a conditional constraint.
6. Fractional relationships between
variables are not permitted in the standard form of a linear program.
7. A business owner is trying to
decide whether to buy, rent, or lease office space and has constructed the
following payoff table based on whether business is brisk or slow. The
conservative (maximin) strategy is:
8. Events that cannot occur at the same
time in any trial of an experiment are:
9. The probability of observing x
successes in a fixed number of trials is a problem related to
10. An equation or inequality that
expresses a resource restriction in a mathematical model is called _____________________.

11. In a break-even model, if all of
the costs are held constant, how does an increase in price affect the model?
12. Steinmetz furniture buys 2
products for resale: big shelves (B) and medium shelves (M). Each big shelf
costs $100 and requires 100 cubic feet of storage space, and each medium shelf
costs $50 and requires 80 cubic feet of storage space. The company has $25000
to invest in shelves this week, and the warehouse has 18000 cubic feet
available for storage. Profit for each big shelf is $85 and for each medium
shelf is $75. What is the storage space constraint?
13. Steinmetz furniture buys 2
products for resale: big shelves (B) and medium shelves (M). Each big shelf
costs $100 and requires 100 cubic feet of storage space, and each medium shelf
costs $50 and requires 80 cubic feet of storage space. The company has $25000
to invest in shelves this week, and the warehouse has 18000 cubic feet
available for storage. Profit for each big shelf is $85 and for each medium
shelf is $75. What is the constraint on money to invest?
14. Given the following linear
programming problem that minimizes cost.
Min Z = 2x + 8y
Subject to 8x + 4y ? 64
2x + 4y ? 32
y ? 2
What is the sensitivity range for
the third constraint, y ? 2?
15. The following is an Excel
“Answer” and “Sensitivity” reports of a linear programming problem:
The Answer Report:
The Sensitivity Report:
Which additional resources would you
recommend to be increased?
16. Let xij = gallons of component i
used in gasoline j. Assume that we have two components and two types of
gasoline. There are 8,000 gallons of component 1 available, and the demands for
gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the
supply constraint for component 1.
17. Compared to transportation LP
problems, assignment problems are unique because
18. The Kirschner Company has a
contract to produce garden hoses for a customer. Kirschner has 5 different
machines that can produce this kind of hose. Write a constraint to ensure that
if machine 4 is used, machine 1 will not be used.
18. If we are solving a 0-1 integer
programming problem, the constraint x1 = x2 is a __________ constraint.
20. Consider the following network
representation of shipment routes between plants, a distribution center, and
retail outlets. The numbers next to the arcs represent shipping costs. For
example, the cost of shipping from plant 1 to distribution center 3 is equal to
2.
21. The following table represents
the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C.
The constraint that represents the quantity supplied by DC 1 is:
22. Professor Truman would like to
assign grades such that 10% of students receive As. If the exam average is 62
with a standard deviation of 13, what grade should be the cutoff for an A?
(Round your answer.)
23. Assume that it takes a college
student an average of 5 minutes to find a parking spot in the main parking lot.
Assume also that this time is normally distributed with a standard deviation of
2 minutes. What percentage of the students will take between 2 and 6 minutes to
find a parking spot in the main parking lot?
24. In the Monte Carlo process,
values for a random variable are generated by __________ a probability
distribution.
25. For the following frequency
distribution of demand, the random number 0.8177 would be interpreted as a
demand of:
26. Consider the following graph of
sales. Which of the following characteristics is exhibited by the data?
27. __________ moving averages react
more slowly to recent demand changes than do __________ moving averages.
28. Students are organizing a
“Battle of the Bands” contest. They know that at least 100 people
will attend. The rental fee for the hall is $200 and the winning band will
receive $500. In order to guarantee that they break even, how much should they charge
for each ticket? (Note: Write your answer with two significant places after the
decimal and do not include the dollar “$” sign. For instance, for five dollars,
write your answer as 5.00).
29. Nixon’s Bed and Breakfast has a
fixed cost of $5000 per month and the revenue they receive from each booked
room is $200. The variable cost per room is $75. How many rooms do they have to
sell each month to break even? (Note: The answer is a whole number. Give the
answer as a whole number, omitting the decimal point. For instance, use 12 for
twelve rooms).
30. Ford’s Bed & Breakfast
breaks even if they sell 50 rooms each month. They have a fixed cost of $6500
per month. The variable cost per room is $30. For this model to work, what must
be the revenue per room? (Note: The answer is a whole dollar amount. Give the
answer as a whole number, omitting the decimal point. For instance, use 105 to
write $105.00).
31. Consider the following linear
program, which maximizes profit for two products, regular (R), and super (S):
A change in the market has increased
the profit on the super product by $5. Total profit will increase by
__________. Write your answers with two significant places after the decimal
and do not include the dollar “$” sign.
32. Consider the following linear
program, which maximizes profit for two products, regular (R), and super (S):
MAX
33. Kitty Kennels provides overnight
lodging for a variety of pets. An attractive feature is the quality of care the
pets receive, including well balanced nutrition. The kennel’s cat food is made
by mixing two types of cat food to obtain the “nutritionally balanced cat
diet.” The data for the two cat foods are as follows:
34. Find the optimal Z value for the
following problem. Do not include the dollar “$” sign with your answer.
Max Z = x1 + 6×2
Subject to: 17×1 + 8×2 ? 136
3×1 + 4×2 ? 36
x1, x2 ? 0 and integer
35. Let’s say that a life insurance
company wants to update its actuarial tables. Assume that the probability
distribution of the lifetimes of the participants is approximately a normal
distribution with a mean of 72 years and a standard deviation of 5 years. What
proportion of the plan participants are expected to survive to see their 75th
birthday? Note: Round your answer, if necessary, to two places after the
decimal. Please express your answer with two places after the decimal.
36. Ms. Hegel is considering four
different opportunities, A, B, C, or D. The payoff for each opportunity will
depend on the economic conditions, represented in the payoff table below.
Investment Economic Conditions Poor
(S1) Average (S2) Good (S3) Excellent (S4)
A 80
15 18
47
B 50
75 35
35
C -90
225 -50
12
D 36
25 25
27
Suppose all states of the world are
equally likely (each state has a probability of 0.25). What is the expected
value of perfect information? Note: Report your answer as an integer, rounding
to the nearest integer, if applicable
37. The local operations manager for
the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates
that net revenues will vary with how well taxpayers comply with the new tax
code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and
0.50 respectively. What is the expected value of perfect information? Do not
include the dollar “$” sign with your answer. The following payoff table is
given in thousands of dollars (e.g. 50 = $50,000). Note: Please express your
answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to
the nearest whole number, if necessary.
38. The local operations manager for
the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates
that net revenues will vary with how well taxpayers comply with the new tax
code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and
0.50 respectively. What are the expected net revenues for the number of workers
he will decide to hire? The following payoff table is given in thousands of dollars
(e.g. 50 = $50,000). Note: Please express your answer as a whole number in
thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if
necessary.
39. Recent past demand for product
ABC is given in the following table.
Month Actual Demand
May 33

June 32
July 39
August 37
The forecasted demand for May, June,
July and August were 25, 30, 33, and 38 respectively. Determine the value of
MAD. Note: Please express the result as a number with 2 decimal places. If necessary,
round your result accordingly. For instance, 9.146, should be expressed as 9.15

40. Consider the following decision tree. The
objective is to choose the best decision among the two available decisions A
and B. Find the expected value of the best decision. Do not include the dollar
“$” sign with your answer.