Strayer MATH540 Final Exam (3 different VERSIONS)

MATH 540 Final Exam (3 different
VERSIONS)
VERSION 1
Validation of a
simulation model occurs when the true steady state average results have been
reached
Excel can be used to
simulate systems that can be represented by both discrete and continuous random
variables
In a total integer
model, all decision variables have integer solution values
Fractional
relationships between variables are not permitted in the standard form of a
linear program
A cycle is an up and
down movement in demand that repeats itself in less than 1 year
In an unbalanced
transportation model, supply does not equal demand and one set of constraints
uses ? signs
The probability of
observing x successes in a fixed number of trials is a problem related to
Using the minimax
regret criterion to make a decision, you
In a break-even model,
if all of the costs are held constant, how does an increase in price affect the
model?
In linear programming
problems, multiple optimal solutions occur
Using the maximin
criterion to make a decision, you
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?
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?
The following is an
Excel “Answer” and “Sensitivity” reports of a linear programming problem:
The production manager
for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources
used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt
per week and at most 3200 oz of wheat per week respectively. Each bottle of
light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark
beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per
bottle, and profits for dark beer are $1 per bottle. What is the optimal weekly
profit?
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.
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?
If we are solving a
0-1 integer programming problem, the constraint x1 = x2 is a
__________ constraint.
In a capital budgeting
problem, if either project 1 or project 2 is selected, then project 5 cannot be
selected. Which of the alternatives listed below correctly models this
situation?
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.
The following table
represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A,
B, or C.
The metropolitan
airport commission is considering the establishment of limitations on noise
pollution around a local airport. At the present time, the noise level
per jet takeoff in one neighborhood near the airport is approximately normally
distributed with a mean of 100 decibels and a standard deviation of 3
decibels. What is the probability that a randomly selected jet will
generate a noise level of more than 105 decibels? Note: please provide
your answer to 2 places past the decimal point, rounding as appropriate.
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.)
__________ moving
averages react more slowly to recent demand changes than do __________ moving
averages.
Consider the following
graph of sales.
For the following
frequency distribution of demand, the random number 0.8177 would be interpreted
as a demand of:
In the Monte Carlo
process, values for a random variable are generated by __________ a probability
distribution.
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).
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).
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).
Consider the following
linear program, which maximizes profit for two products, regular (R), and super
(S):
Tracksaws, Inc. makes
tractors and lawn mowers. The firm makes a profit of $30 on each tractor and
$30 on each lawn mower, and they sell all they can produce. The time
requirements in the machine shop, fabrication, and tractor assembly are given
in the table.
Kitty Kennels provides
overnight lodging for a variety of pets. An attractive feature is the quality
of care the pets receive, including well balanced nutrition. The kennel’s cat
food is made by mixing two types of cat food to obtain the “nutritionally
balanced cat diet.” The data for the two cat foods are as follows:
Find the optimal Z
value for the following problem. Do not include the dollar “$” sign with your
answer.
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.
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.
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 =
$50,000). Round to the nearest whole number, if necessary.
The local operations
manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers.
He estimates that net revenues will vary with how well taxpayers comply with
the new tax code. The probabilities of low, medium, and high compliance are
0.20, 0.30, and 0.50 respectively. What is the expected value of perfect
information? Do not include the dollar “$” 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 = $50,000). Round to the nearest whole number, if
necessary.
The following sales
data are available for 2003-2008 :
Consider the following
decision tree. The objective is to choose the best decision among the two
available decisions A and B. Find the expected value of the best decision. Do
not include the dollar “$” sign with your answer
VERSION 2
Adjusted exponential
smoothing is an exponential smoothing forecast adjusted for seasonality.
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
Fractional
relationships between variables are not permitted in the standard form of a
linear program
In an unbalanced
transportation model, supply does not equal demand and one set of constraints
uses ? signs.
In a total integer
model, all decision variables have integer solution values
A cycle is an up and
down movement in demand that repeats itself in less than 1 year
Using the maximin
criterion to make a decision, you
Events that cannot
occur at the same time in any trial of an experiment are
Using the minimax
regret criterion to make a decision, you
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 probability of
observing x successes in a fixed number of trials is a problem related to
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 objective function?
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?
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:
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?
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.
An appropriate part of the model would be
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?
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
If we are solving a
0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.
The following table
represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A,
B, or C.
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?
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.)
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:
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?
__________ moving
averages react more slowly to recent demand changes than do __________ moving
averages.
Consider the following
graph of sales.
Which of the following
characteristics is exhibited by the data?
For the following
frequency distribution of demand, the random number 0.8177 would be interpreted
as a demand of:
Carter’s Bed &
Breakfast breaks even every month if they book 30 rooms over the course of a
month. Their fixed cost is $1050 per month and the revenue they receive from
each booked room is $150. What is the variable cost per occupied 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).
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).
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).
Tracksaws, Inc. makes
tractors and lawn mowers. The firm makes a profit of $30 on each tractor and
$30 on each lawn mower, and they sell all they can produce. The time
requirements in the machine shop, fabrication, and tractor assembly are given
in the table
Tracksaws, Inc. makes
tractors and lawn mowers. The firm makes a profit of $30 on each tractor and
$30 on each lawn mower, and they sell all they can produce. The time
requirements in the machine shop, fabrication, and tractor assembly are given
in the table
Kitty Kennels provides
overnight lodging for a variety of pets. An attractive feature is the quality
of care the pets receive, including well balanced nutrition. The kennel’s cat
food is made by mixing two types of cat food to obtain the “nutritionally
balanced cat diet.” The data for the two cat foods are as follows
Find the optimal Z
value for the following problem. Do not include the dollar “$” sign with your
answer
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
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
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 = $50,000). Round to the nearest
whole number, if necessary
The local operations
manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers.
He estimates that net revenues will vary with how well taxpayers comply with
the new tax code. The probabilities of low, medium, and high compliance are
0.20, 0.30, and 0.50 respectively. What is the expected value of perfect
information? Do not include the dollar “$” 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 =
$50,000). Round to the nearest whole number, if necessary
The following sales
data are available for 2003-2008
Calculate the MAPD and
express it in decimal notation. Please express the result as a number with 4
decimal places. If necessary, round your result accordingly. For instance,
9.14677, should be expressed as 9.1468
Consider the following
decision tree. The objective is to choose the best decision among the two
available decisions A and B. Find the expected value of the best decision. Do
not include the dollar “$” sign with your answer

VERSION 3
In general, an
increase in price increases the break even point if all costs are held constant.
The feasible solution
area contains infinite solutions to the linear program
A change in the value
of an objective function coefficient will always change the value of the
optimal solution.
When using a linear
programming model to solve the “diet” problem, the objective is generally to
maximize nutritional content.
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 can not be
selected.
In a transshipment
problem, items may be transported from destination to destination and from
source to source.
The events in an
experiment are mutually exclusive if only one can occur at a time
The minimax criterion
minimizes the maximum payoff.
Excel can be used to simulate
systems that can be represented by both discrete and continuous random
variables.
A cycle is an up and
down movement in demand that repeats itself in less than 1 year.
A bed and breakfast
even every month if they book 30 rooms over the course of a month. Their
fixed cost is $6000 per month and the revenue they receive from each booked
room is $180. What is the variable cost per occupied room?
If the price decreases
but fixed and variable costs do not change, the break even point
Cully furniture buys 2
products for resale: big shelves (B) and medium shelves (M). Each big shelf
costs $500 and requires 100 cubic feet of storage space, and each medium shelf
costs $300 and requires 90 cubic feet of storage space. The company has $75000
to invest in shelves this week, and the warehouse has 18000 cubic feet
available for storage. Profit for each big shelf is $300 and for each medium
shelf is $150. What is the objective function?
Cully furniture buys 2
products for resale: big shelves (B) and medium shelves (M). Each big shelf
costs $500 and requires 100 cubic feet of storage space, and each medium shelf
costs $300 and requires 90 cubic feet of storage space. The company has $75000
to invest in shelves this week, and the warehouse has 18000 cubic feet available
for storage. Profit for each big shelf is $300 and for each medium shelf is
$150. In order to maximize profit, how many big shelves (B) and how many medium
shelves (M) should be purchased?
The following is an
Excel “Answer” and “Sensitivity” reports of a linear programming problem:
Given the following
linear programming problem that minimizes cost.
Min Z = 2x + 8y
Subject to 8x + 4y ? 64
2x + 4y ? 32
y ? 2
Compared to blending
and product mix problems, transportation problems are unique because
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
demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write
the supply constraint for component 1.
If we are solving a
0-1 integer programming problem, the constraint x1 = x2 is a
__________ constraint
The Wiethoff Company
has a contract to produce garden hoses for a customer. Wiethoff has 4 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
The assignment problem
constraint x31+x32+x33+x34 ? 2 means
The following table
represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A,
B, or C
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
Jim 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
20% for University X and 45% for University Y. What is the probability that Jim
will not be accepted at either university?
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
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
A bakery is
considering hiring another clerk to better serve customers. To help with
this decision, records were kept to determine how many customers arrived in
10-minute intervals. Based on 100 ten-minute intervals, the following
probability distribution and random number assignments developed
For the following
frequency distribution of demand, the random number 0.8177 would be interpreted
as a demand of
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?
A production process
requires a fixed cost of $50,000. The variable cost per unit is $25 and the
revenue per unit is projected to be $45. Find the break-even point
Tracksaws, Inc. makes
tractors and lawn mowers. The firm makes a profit of $30 on each tractor and
$30 on each lawn mower, and they sell all they can produce. The time
requirements in the machine shop, fabrication, and tractor assembly are given
in the table
Consider the following
linear program, which maximizes profit for two products, regular (R), and super
(S):
MAX
50R + 75S
s.t.
1.2R + 1.6 S ? 600 assembly (hours)
0.8R + 0.5 S ? 300 paint (hours)
.16R + 0.4 S ? 100 inspection (hours)
Kitty Kennels provides
overnight lodging for a variety of pets. An attractive feature is the quality
of care the pets receive, including well balanced nutrition. The kennel’s cat
food is made by mixing two types of cat food to obtain the “nutritionally
balanced cat diet.” The data for the two cat foods are as follows
Find the optimal Z
value for the following problem. Do not include the dollar “$” sign with your
answer.
MAX Z = 5×1 + 8×2
s.t.
x1 + x2 ? 6
5×1 + 9×2 ? 45
x1, x2 ? 0 and integer
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 “$” sign with your answer
An investor is
consider 4 different opportunities, A, B, C, or D. The payoff for each
opportunity will depend on the economic conditions, represented in the payoff
table below
The local operations
manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers.
He estimates that net revenues will vary with how well taxpayers comply with
the new tax code. The probabilities of low, medium, and high compliance are
0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the
number of workers he will decide to hire? Do not include the dollar “$” sign
with your answer
The following sales
data are available for 2003-2008