QUESTION 1
A croissant shop produces two products: bear claws (B) and almond-filled
croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast,
and 2 TS of almond paste. An almond-filled croissant requires 3 ounces of
flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600
ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste
available for today’s production run. Bear claw profits are 20 cents each, and
almond-filled croissant profits are 30 cents each. What is the optimal daily
profit?
$38
0
$40
0
$42
0
$44
0
1 points
QUESTION 2
A systematic approach to model formulation is to first
construct the objective function .
develop each constraint separately.
define decision variables.
determine the right hand side of each
constraint.
1 points
QUESTION 3
Balanced transportation problems have the following type of constraints:
=
<
1 points
QUESTION 4
Compared to blending and product mix problems, transportation problems
are unique because
they maximize profit.
the constraints are all equality constraints with no " " or
" " constraints.
they contain fewer variables.
the solution values are always integers.
1 points
QUESTION 5
In a multiperiod scheduling problem, the production constraint usually takes
the form of:
beginning inventory
ending inventory
beginning inventory
ending inventory
beginning inventory
= production
beginning inventory
ending inventory
+ demand – production =
– demand + production =
– ending inventory + demand
+ demand + production =
1 points
QUESTION 6
In a portfolio problem, x1, x2, and x3 represent the number of shares
purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25,
and $110, respectively. The investor has up to $50,000 to invest.
The stockbroker suggests limiting the investments so that no more than
$10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3
does not exceed 350, whichever is more restrictive. How would this be
formulated as a linear programming constraint?
X2 10000
X2 + X3 350
10,000 X2
350X2 +
350X3
47.25X2 10,000
X2 + X3
350
47.25X2 10,000
47.25 X2 + 110X3
350
1 points
QUESTION 7
In a portfolio problem, x1, x2, and x3 represent the number of shares
purchased of stocks 1, 2, and 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:
15X1 + 47.25X2 +110 X3 50,000
MAX 15X1 + 47.25X2 + 110X3
X1 + X2 +X3 50,000
MAX 50(15)X1 + 50 (47.25)X2 + 50
(110)X3
1 points
QUESTION 8
Let:?rj?= regular production quantity for period?j,?oj?=overtime production quantity in
period?j,?ij?= inventory quantity in period?j, and?dj?= demand quantity in period?j. Correct
formulation of the demand constraint for a multiperiod scheduling problem is:
rj + oj + i2 – i1
dj
rj + oj + i1 – i2
dj
rj + oj + i1 – i2
dj
rj – oj – i1 + i2
dj
1 points
QUESTION 9
Let xij = gallons of component i used in gasoline j. Assume that we have two
components and two types of gasoline. There are 8000 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.
x21 + x22
8
000
x12 + x22
8
000
x11 + x12
8
000
x21 + x22
8
000
1 points
QUESTION 10
Quickbrush Paint Company is developing a linear program to determine the
optimal quantities of ingredient A and ingredient B to blend together to make
oil-base and water-base paint. The oil-base paint contains 90 percent A and
10 percent B, whereas the water-base paint contains 30 percent A and 70
percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000
gallons of ingredient B in inventory and cannot obtain more at this time.
Assuming that x represents the number of gallons of oil-base paint,
and y represents the gallons of water-base paint, which constraint is correctly
represents the constraint on ingredient A?
.9A + .1B
10,000
.9x + .1y
10,000
.3x + .7y
10,000
.9x + .3y
10,000
1 points
QUESTION 11
Spring is right around the corner and that can mean only one thing: it’s time
to incubate some eggs for a fresh crop of chickens to supplement the
existing flock for the year. There are three breeds that are popular: Leghorns,
Buff Orpingtons, and Cochins, and each has its own strengths and
weaknesses. The Leghorns, for example, are superb layers but easily
excitable. The Cochins, on the other hand, are very even-tempered but not
the best layers. They do have marvelous plumage, with feathers that extend
down to their feet. The Buff Orpingtons are good layers, have interesting
plumage, and are mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs
as possible while keeping the noise to a dull roar and having a nice array of
birds free-ranging on his lawn during those lazy summer days. He has put
the relevant data in table form. Plumage numbers are on a scale from 1-10,
with 10 being the most desirable. The egg output is not on a scale, but is
instead the average output for the breed, based on years of collecting eggs.
Temperament is actually measured by the average volume of cackling,
clucking, and crowing and is measured in decibels per bird. Appetite is
measured in ounces of layer pellets per week consumed by each of the
breeds, while fertilizer is measured as the output in ounces per week.
Which of the following is an appropriate objective function?
Max Z = 5L + 2C +
4.5B
Max Z = 10L + 10C
+ 10B
Min Z = 5L + 2C +
4.5B
Min Z = 10L + 10C +
10B
1 points
QUESTION 12
Spring is right around the corner and that can mean only one thing: it’s time
to incubate some eggs for a fresh crop of chickens to supplement the
existing flock for the year. There are three breeds that are popular: Leghorns,
Buff Orpingtons, and Cochins, and each has its own strengths and
weaknesses. The Leghorns, for example, are superb layers but easily
excitable. The Cochins, on the other hand, are very even-tempered but not
the best layers. They do have marvelous plumage, with feathers that extend
down to their feet. The Buff Orpingtons are good layers, have interesting
plumage, and are mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs
as possible while keeping the noise to a dull roar and having a nice array of
birds free-ranging on his lawn during those lazy summer days. He has put
the relevant data in table form. Plumage numbers are on a scale from 1-10,
with 10 being the most desirable. The egg output is not on a scale, but is
instead the average output for the breed, based on years of collecting eggs.
Temperament is actually measured by the average volume of cackling,
clucking, and crowing and is measured in decibels per bird. Appetite is
measured in ounces of layer pellets per week consumed by each of the
breeds, while fertilizer is measured as the output in ounces per week.
The poultry farmer would like to generate 80 ounces of fertilizer per week
while feeding a maximum of 160 ounces of layer pellets each week. Which of
these constraints is correct?
3L + 2C + 4C
80
5L + 4C + 8B
160
5L + 4C + 8B
160
5L + 4C +8B
80
1 points
QUESTION 13
Spring is right around the corner and that can mean only one thing: it’s time
to incubate some eggs for a fresh crop of chickens to supplement the
existing flock for the year. There are three breeds that are popular: Leghorns,
Buff Orpingtons, and Cochins, and each has its own strengths and
weaknesses. The Leghorns, for example, are superb layers but easily
excitable. The Cochins, on the other hand, are very even-tempered but not
the best layers. They do have marvelous plumage, with feathers that extend
down to their feet. The Buff Orpingtons are good layers, have interesting
plumage, and are mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs
as possible while keeping the noise to a dull roar and having a nice array of
birds free-ranging on his lawn during those lazy summer days. He has put
the relevant data in table form. Plumage numbers are on a scale from 1-10,
with 10 being the most desirable. The egg output is not on a scale, but is
instead the average output for the breed, based on years of collecting eggs.
Temperament is actually measured by the average volume of cackling,
clucking, and crowing and is measured in decibels per bird. Appetite is
measured in ounces of layer pellets per week consumed by each of the
breeds, while fertilizer is measured as the output in ounces per week.
The poultry farmer has in mind the following levels for each of his metrics of
interest: a plumage score greater than 75, fertilizer production greater than
80 ounces per week, temperment less than 100 decibels, and an appetite
less than 160 ounces of layer pellets per week. When he runs his linear
programming model, he discovers that his flock will consist entirely of
Leghorn birds. He can picture the sad little faces of his children when he tells
them that there will be no variety of birds gracing their front lawn this
summer. Help him avoid the embarrassment by selecting a constraint that
will ensure that there is some variety in his flock.
5L + 4C + 8B
160
5L + 4C + 8B
160
C+B
5
L+C+B
5
1 points
QUESTION 14
Spring is right around the corner and that can mean only one thing: it’s time to incubate
some eggs for a fresh crop of chickens to supplement the existing flock for the year. There
are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its
own strengths and weaknesses. The Leghorns, for example, are superb layers but easily
excitable. The Cochins, on the other hand, are very even-tempered but not the best layers.
They do have marvelous plumage, with feathers that extend down to their feet. The Buff
Orpingtons are good layers, have interesting plumage, and are mid-range in their
temperament.
The chicken farmer would like this crop of chickens to produce as many eggs as possible
while keeping the noise to a dull roar and having a nice array of birds free-ranging on his
lawn during those lazy summer days. He has put the relevant data in table form. Plumage
numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not
on a scale, but is instead the average output for the breed, based on years of collecting
eggs.
Temperament is actually measured by the average volume of cackling, clucking, and crowing
and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per
week consumed by each of the breeds, while fertilizer is measured as the output in ounces
per week.
When the poultry farmer runs his linear programming model, he discovers that his flock will
consist entirely of Leghorn birds. He studies his sensitivity report (copied below) and decides
to write a constraint that requires two Cochin chickens to be selected. If the current optimal
mix of breeds results in 160 eggs per week, which of the following statements is best?
The new weekly egg output will
be 169.
The new weekly egg output will
be 162.
The new weekly egg output will
be 158.
The new weekly egg output will
be 154.
1 points
QUESTION 15
Spring is right around the corner and that can mean only one thing: it’s time
to incubate some eggs for a fresh crop of chickens to supplement the
existing flock for the year. There are three breeds that are popular: Leghorns,
Buff Orpingtons, and Cochins, and each has its own strengths and
weaknesses. The Leghorns, for example, are superb layers but easily
excitable. The Cochins, on the other hand, are very even-tempered but not
the best layers. They do have marvelous plumage, with feathers that extend
down to their feet. The Buff Orpingtons are good layers, have interesting
plumage, and are mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs
as possible while keeping the noise to a dull roar and having a nice array of
birds free-ranging on his lawn during those lazy summer days. He has put
the relevant data in table form. Plumage numbers are on a scale from 1-10,
with 10 being the most desirable. The egg output is not on a scale, but is
instead the average output for the breed, based on years of collecting eggs.
Temperament is actually measured by the average volume of cackling,
clucking, and crowing and is measured in decibels per bird. Appetite is
measured in ounces of layer pellets per week consumed by each of the
breeds, while fertilizer is measured as the output in ounces per week.
The poultry farmer has in mind the following levels for each of his metrics of
interest: a plumage score greater than 75, fertilizer production greater than
80 ounces per week, temperment less than 100 decibels, and an appetite
less than 160 ounces of layer pellets per week. Use this portion of the
sensitivity report to evaluate the following statements:
The noise level around the farm should be over 60
decibels.
The fertilizer generated will be 160 ounces per
week.
Layer pellets will be consumed at the rate of 96
ounces per week.
The plumage score will be less than 40.
1 points
QUESTION 16
In a portfolio problem, x1, x2, and x3 represent the number of shares
purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25,
and $110, respectively. The investor has up to $50,000 to invest.
The expected returns on investment of the three stocks are 6%, 8%, and
11%. An appropriate objective function is:
MAX .06X1 +.08X2 +.11X3
MAX .
06(15)X1 +.08(47.25)X2 +.11(110)
X3
MAX 15X1 + 47.25X2 +.110X3
MAX (1/.06)X1 +.(1/08)X2 +
(1/.11)X3
1 points
QUESTION 17
In a portfolio problem, x1, x2, and x3 represent the number of shares
purchased of stocks 1, 2, and 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?
X1 0.35
X1 = 0.35 (50000)
X1 0.35(X1 + X2 +
X 3)
X1 = 0.35(X1 + X2 +
X 3)
1 points
QUESTION 18
The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V).
He has a limited amount of the three ingredients used to produce these chips
available for his next production run: 4800 ounces of salt, 9600 ounces of
flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of
salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of
vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of
herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips
$0.50.
For the production combination of 800 bags of lime and 600 bags of vinegar,
which of the three resources is (are) not completely used?
flour only
salt only
herbs only
salt and
flour
1 points
QUESTION 19
The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V).
He has a limited amount of the three ingredients used to produce these chips
available for his next production run: 4800 ounces of salt, 9600 ounces of
flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of
salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of
vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of
herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips
$0.50.
What is the constraint for salt?
6L + 8V
4800
1L + 2V
4800
3L + 2V
4800
2L + 3V
4800
1 points
QUESTION 20
The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V).
He has a limited amount of the three ingredients used to produce these chips
available for his next production run: 4800 ounces of salt, 9600 ounces of
flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of
salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of
vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of
herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips
$0.50.
Which of the following is not a feasible production combination?
0L and 0V
0L and
1000V
1000L and
0V
0L and
1200V
1 points
QUESTION 21
The production manager for the Softy soft drink company is considering the
production of two kinds of soft drinks: regular and diet. Two of her resources
are production time (8 hours = 480 minutes per day) and syrup (1 of the
ingredients) limited to 675 gallons per day. To produce a regular case
requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes
and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and
profits for diet soft drink are $2.00 per case. What is the time constraint?
2R + 4D
480
2D + 4R
480
2R + 3D
480
3R + 2D
480
1 points
QUESTION 22
The production manager for the Softy soft drink company is considering the
production of two kinds of soft drinks: regular and diet. Two of her resources
are constraint production time (8 hours = 480 minutes per day) and syrup (1
of the ingredients), limited to 675 gallons per day. To produce a regular case
requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes
and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and
profits for diet soft drink are $2.00 per case. What is the optimal daily profit?
$27
0
$32
0
$42
0
$52
0
1 points
QUESTION 23
The type of linear program that compares services to indicate which one is
less productive or inefficient is called
product mix
data envelopment
analysis
marketing
blending
1 points
QUESTION 24
When systematically formulating a linear program, the first step is to
construct the objective
function.
formulate the
constraints.
identify the decision
variables.
identify the parameter
values.
1 points
QUESTION 25
Assume that x2, x7 and x8 are the dollars invested in three different common
stocks from New York Stock Exchange. In order to diversify the investments,
the investing company requires that no more than 60% of the dollars
invested can be in "stock 2". The constraint for this requirement can be
written as:
x2 .60
x2 .60
(x2 + x7 + x8)
.4×2 – .6×7 – .
6×8 0
.4×2 – .6×7 – .
6×8 0
1 points
QUESTION 26
If xab = the production of product a in period b, then to indicate that the limit
on production of the company’s 3 products in period 2 is 400, we write:
X32 400
X21 + X22 + X23
400
X12 + X22 + X32
400
X12 + X22 + X32
400
1 points
QUESTION 27
Let xij = gallons of component i used in gasoline j. Assume that we have two
components and two types of gasoline. There are 8000 gallons of component
1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000
gallons, respectively. Write the demand constraint for gasoline type 1.
x21 + x22 =
11000
x12 + x22 =
11000
x11 + x21 11
000
x11 + x21 =
11000
1 points
QUESTION 28
Let xij = gallons of component i used in gasoline j. Assume that we have two
components and two types of gasoline. There are 8000 gallons of component
1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000
gallons, respectively. Write the constraint stating that the component 1
cannot account for more than 35% of the gasoline type 1.
x11 + x12 (.35)
(x11 + x21)
x11 + .35(x11 + x12)
-.65×11 + .35×21 0
.65×11 – .35×21 0
1 points
QUESTION 29
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.
The constraint for ingredient 3 is:
.5A + .75B
= 20
.3B = 20
.3B 20
.3B
20
1 points
QUESTION 30
In a balanced transportation model, supply equals demand such that all
constraints can be treated as equalities.
True
False
1 points
