MATH
540- WEEK 11 FINAL EXAM
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5 out of 5 points
A cycle is an up and down movement in demand
that repeats itself in less than 1 year.
Question 2
5 out of 5 points
Adjusted
exponential smoothing is an exponential smoothing forecast adjusted for
seasonality.
Question 3
5 out of 5 points
In
a total integer model, all decision variables have integer solution values.
Question 4
5 out of 5 points
Fractional
relationships between variables are not permitted in the standard form of a
linear program.
Question 5
5 out of 5 points
Excel
can be used to simulate systems that can be represented by both discrete and
continuous random variables.
Question 6
5 out of 5 points
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.
Question 7
5 out of 5 points
Events
that cannot occur at the same time in any trial of an experiment are:
Question 8
5 out of 5 points
Using
the minimax regret criterion to make a decision, you
Answer
Question 9
5 out of 5 points
The
probability of observing x
successes in a fixed number of trials is a problem related to
Question 10
5 out of 5 points
Using
the maximin criterion to make a decision, you
Question 11
5 out of 5 points
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.
Question 12
5 out of 5 points
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?
Question 13
5 out of 5 points
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?
Question 14
5 out of 5 points
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?
Question 15
5 out of 5 points
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:
Question 16
5 out of 5 points
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?
Question 17
5 out of 5 points
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.
Ingredient
Percent per pound in Feed A
Percent per pound in Feed B
Minimum daily requirement (pounds)
1
20
24
30
2
30
10
50
3
0
30
20
4
24
15
60
5
10
20
40
The constraint for
ingredient 3 is:
Question 18
5 out of 5 points
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.
Question 19
5 out of 5 points
If
we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________
constraint.
Question 20
0 out of 5 points
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.
Question 21
0 out of 5 points
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.
Assume that Plant 1 can supply 400 units and
Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units;
Outlet 5, 250 units; Outlet 6, 450 units. Supply is less than demand, so this
is an unbalanced transshipment model. Which constraint represents the
quantity shipped to retail outlet 6?
Question 22
5 out of 5 points
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.)
Answer
Question 23
5 out of 5 points
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:
Question 24
5 out of 5 points
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?
Question 25
5 out of 5 points
For
the following frequency distribution of demand, the random number 0.8177 would
be interpreted as a demand of:
Question 26
5 out of 5 points
__________
moving averages react more slowly to recent demand changes than do __________
moving averages.
Question 27
5 out of 5 points
Consider
the following graph of sales.
Which of the following
characteristics is exhibited by the data?
Question 28
5 out of 5 points
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).
Question 29
5 out of 5 points
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).
Question 30
5 out of 5 points
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).
Question 31
0 out of 5 points
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:
Final
Reduced
Objective
Allowable
Allowable
Cell
Name
Value
Cost
Coefficient
Increase
Decrease
$B$7 Regular
= 291.67 0.00
50
70
20
$C$7 Super
= 133.33 0.00
75
50
43.75
Final
Shadow
Constraint
Allowable
Allowable
Cell
Name
Value
Price
R.H. Side
Increase
Decrease
$E$3
Assembly (hr/unit) 563.33
0.00 600
1E+30
36.67
$E$4
Paint (hr/unit) 300.00
33.33 300
39.29
175
$E$5
Inspect (hr/unit) 100.00
145.83 100
12.94
40
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.
Question 32
0 out of 5 points
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:
Final
Reduced
Objective
Allowable
Allowable
Cell
Name
Value
Cost
Coefficient
Increase
Decrease
$B$7 Regular
= 291.67 0.00
50
70
20
$C$7 Super
= 133.33 0.00
75
50
43.75
If downtime reduced the
available capacity for painting by 40 hours (from 300 to 260 hours), profits
would be reduced by __________. Write your answers with two significant places
after the decimal and do not include the dollar “$” sign.
Evaluation Method Correct Answer
Case Sensitivity
Exact Match
1333
Exact Match
1,333
Question 33
5 out of 5 points
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:
Cat Food
Cost/oz
protien (%)
fat (%)
Partner's Choice $0.20
45
20
Feline Excel $0.15
15
30
Klein Kennels wants to be
sure that the cats receive at least 5 ounces of protein and at least 3 ounces
of fat per day. What is the optimal cost of this plan? Note: Please write your answers
with two significant places after the decimal and do not include the dollar “$”
sign. For instance, $9.45 (nine dollars and fortyfive cents) should be
written as 9.45
Question 34
5 out of 5 points
Find
the optimal Z value for the following problem. Do not include the dollar “$”
sign with your answer.
MAX Z = 5x1 + 8x2
s.t.
x1 + x2
≤ 6
5x1 + 9x2 ≤ 45
x1, x2 ≥ 0 and integer
Question 35
0 out of 5 points
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.
Question 36
5 out of 5 points
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.
Investment Economic
Conditions
Poor
(S1)
Average
(S2)
Good
(S3)
Excellent
(S4)
A 18
25
50
80
B 19
100
50
75
C 100
26
120
60
D 20
27
50
240
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
Question 37
5 out of 5 points
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 = $50,000). Round to
the nearest whole number, if necessary.
Question 38
5 out of 5 points
The
local operations manager for the IRS must decide whether to hire 1, 2, or 3
temporary workers. He estimates that net revenues will vary with how well
taxpayers comply with the new tax code. The probabilities of low, medium, and
high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected
value of perfect information? Do not include the dollar “$” 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 =
$50,000). Round to the nearest whole number, if necessary.
Question 39
0 out of 5 points
The
following sales data are available for 2003-2008 :
Year
Sales
Forecast
2003
7
7
2004
8
8.5
2005
12
10.5
2006
14
13
2007
16
15
2008
18
16
Calculate the MAPD and
express it in decimal notation. Please express the result as a number with 4 decimal
places. If necessary, round your result accordingly. For instance, 9.14677,
should be expressed as 9.1468
Question 40
5 out of 5 points
Consider
the following decision tree. The objective is to choose the best decision among
the two available decisions A and B. Find the expected value of the best
decision. Do not include the dollar “$” sign with your answer.
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