MATH 540 WEEK 11 FINAL EXAM
MATH 540 Week 11 Final
Exam
1.
A cycle is an up
and down movement in demand that repeats itself in less than 1 year.
2.
Adjusted
exponential smoothing is an exponential smoothing forecast adjusted for
seasonality.
3.
In a total
integer model, all decision variables have integer solution values.
4.
Fractional
relationships between variables are not permitted in the standard form of a
linear program.
5.
Excel can be
used to simulate systems that can be represented by both discrete and
continuous random variables.
6.
In a 0-1 integer
programming problem involving a capital budgeting application (where xj =
1, if project j is selected, xj = 0, otherwise) the constraint x1 –
x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be
selected.
7.
Events that
cannot occur at the same time in any trial of an experiment are:
8.
Using the
minimax regret criterion to make a decision, you
9.
The probability
of observing x
successes in a fixed number of trials is a problem related to
successes in a fixed number of trials is a problem related to
10.
Using the
maximin criterion to make a decision, you
11. 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:
The conservative (maximin) strategy is:
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. In order to maximize profit, how many big shelves (B) and
how many medium shelves (M) should be purchased?
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?
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.
For a
maximization problem, assume that a constraint is binding. If the original
amount of a resource is 4 lbs., and the range of feasibility (sensitivity
range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of
this resource by 1 lb. will result in the:
16. In a portfolio problem, X1, X2, and X3 represent the number of shares
purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and
$110, respectively. The investor has up to $50,000 to invest. The
investor stipulates that stock 1 must not account for more than 35% of the
number of shares purchased. Which constraint is correct?
17.
The owner of
Black Angus Ranch is trying to determine the correct mix of two types of beef
feed, A and B which cost 50 cents and 75 cents per pound, respectively.
Five essential ingredients are contained in the feed, shown in the table below.
The table also shows the minimum daily requirements of each ingredient.
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 the constraint
that indicates they have to use at least three of the five machines in their
production.
19.
If we are
solving a 0-1 integer programming problem, the constraint x1 = x2 is
a __________ constraint.
20.
A professor
needs help from 3 student helpers to complete 4 tasks. The first task is
grading; the second is scanning; the third is copying, and the fourth is
organizing student portfolios. The estimated time for each student to do
each task is given in the matrix below. Which of the following constraints
represents the assignment for student A?
21.
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.
22. Professor Dewey would like to assign grades such that 15% 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. Jack is considering pursuing an MS in Information Systems degree. He has
applied to two different universities. The acceptance rate for applicants with
similar qualifications is 30% for University X and 60% for University Y. The
decisions of each university have no effect on each other. This means that they
are:
24.
Given an actual
demand of 59, a previous forecast of 64, and an alpha of .3, what would the
forecast for the next period be using simple exponential smoothing?
25.
For the
following frequency distribution of demand, the random number 0.8177 would be
interpreted as a demand of:
26.
__________
moving averages react more slowly to recent demand changes than do __________
moving averages.
27.
Consider the
following graph of sales. Which of the following characteristics is
exhibited by the data?
28.
Joseph is
considering pursuing an MS in Information Systems degree. He has applied to two
different universities. The acceptance rate for applicants with similar
qualifications is 30% for University X and 60% for University Y. What is the probability
that Jim will not be accepted at either university? (Note:
write your answer as a probability, with two decimal places. If
necessary, round to two decimal places. For instance, a probability of
0.252 should be written as 0.25).
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 $105.00).
31.
Consider the
following linear program, which maximizes profit for two products, regular (R),
and super (S):
MAX
50R + 75S
s.t.
1.2R + 1.6 S ≤ 600 assembly (hours)
0.8R + 0.5 S ≤ 300 paint (hours)
.16R + 0.4 S ≤ 100 inspection (hours)
Sensitivity Report:
MAX
50R + 75S
s.t.
1.2R + 1.6 S ≤ 600 assembly (hours)
0.8R + 0.5 S ≤ 300 paint (hours)
.16R + 0.4 S ≤ 100 inspection (hours)
Sensitivity Report:
32.
Consider the
following linear program, which maximizes profit for two products, regular (R),
and super (S):
MAX
50R + 75S
s.t.
1.2R + 1.6 S ≤ 600 assembly (hours)
0.8R + 0.5 S ≤ 300 paint (hours)
.16R + 0.4 S ≤ 100 inspection (hours)
Sensitivity Report:
MAX
50R + 75S
s.t.
1.2R + 1.6 S ≤ 600 assembly (hours)
0.8R + 0.5 S ≤ 300 paint (hours)
.16R + 0.4 S ≤ 100 inspection (hours)
Sensitivity Report:
33.
Klein Kennels
provides overnight lodging for a variety of pets. An attractive feature is the
quality of care the pets receive, including well balanced nutrition. The
kennel’s cat food is made by mixing two types of cat food to obtain the
“nutritionally balanced cat diet.” The data for the two cat foods are as
follows:
34.
Find the optimal
Z value for the following problem. Do not include the dollar “$” sign with your
answer.
MAX Z = 5x1 + 8x2
s.t. x1 + x2 ≤ 6
5x1 + 9x2 ≤ 45
x1, x2 ≥ 0 and integer
MAX Z = 5x1 + 8x2
s.t. x1 + x2 ≤ 6
5x1 + 9x2 ≤ 45
x1, x2 ≥ 0 and integer
35.
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 68 years and a standard deviation of 4 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. James 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.
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 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 =
$50,000). Round to the nearest whole number, if necessary.
38. The local operations manager for the IRS must decide whether to hire 1, 2,
or 3 temporary workers. He estimates that net revenues will vary with how well
taxpayers comply with the new tax code. The probabilities of low, medium, and
high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected
value of perfect information? Do not include the dollar “$” 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 = $50,000). Round to the nearest
whole number, if necessary.
39.
The following
sales data are available for 2003-2008 :
|
·
Year
|
·
Sales
|
·
Forecast
|
|
·
2003
|
·
7
|
·
7
|
|
·
2004
|
·
8
|
·
8.5
|
|
·
2005
|
·
12
|
·
10.5
|
|
·
2006
|
·
14
|
·
13
|
|
·
2007
|
·
16
|
·
15
|
|
·
2008
|
·
18
|
·
16
|
1.
Calculate the MAPD and express it in decimal notation. Please express the result as a number with 4 decimal places. If necessary, round your result accordingly. For instance, 9.14677, should be expressed as 9.1468
Calculate the MAPD and express it in decimal notation. Please express the result as a number with 4 decimal places. If necessary, round your result accordingly. For instance, 9.14677, should be expressed as 9.1468
2. Consider the following decision tree. The objective is to choose the best
decision among the two available decisions A and B. Find the expected value of
the best decision. Do not include the dollar “$” sign with your answer.
