Download Introduction to Management Science, 10e (Taylor)

Introduction to Management Science, 10e (Taylor)
Chapter 4 Linear Programming: Modeling Examples
1) When formulating a linear programming problem constraint, strict inequality signs (i.e., less
than < or, greater than >) are not allowed.
Answer: TRUE
Diff: 2
Page Ref: Ch 2 review
Main Heading: Formulation and Computer Solution
Key words: formulation
2) When formulating a linear programming model on a spreadsheet, the measure of performance
is located in the target cell.
Answer: TRUE
Diff: 2
Page Ref: Ch 2 review
Main Heading: Formulation and Computer Solution
Key words: spreadsheet solution
3) The standard form for the computer solution of a linear programming problem requires all
variables to be to the right and all numerical values to be to the left of the inequality or equality
sign
Answer: FALSE
Diff: 2
Page Ref: Ch 2 review
Main Heading: Formulation and Computer Solution
Key words: formulation, standard form
4) The standard form for the computer solution of a linear programming problem requires all
variables to be on the left side, and all numerical values to be on the right side of the inequality
or equality sign.
Answer: TRUE
Diff: 2
Page Ref: Ch 2 review
Main Heading: Formulation and Computer Solution
Key words: formulation, standard form
5) Fractional relationships between variables are not permitted in the standard form of a linear
program.
Answer: TRUE
Diff: 2
Page Ref: Ch 2 review
Main Heading: Formulation and Computer Solution
Key words: formulation, standard form
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6) A constraint for a linear programming problem can never have a zero as its right-hand-side
value.
Answer: FALSE
Diff: 2
Page Ref: Ch 2 review
Main Heading: Formulation and Computer Solution
Key words: formulation, standard form
7) The right hand side of constraints cannot be negative.
Answer: FALSE
Diff: 2
Page Ref: Ch 2 review
Main Heading: Formulation and Computer Solution
Key words: formulation
8) A systematic approach to model formulation is to first define decision variables.
Answer: TRUE
Diff: 1
Page Ref: Ch 2 review
Main Heading: Formulation and Computer Solution
Key words: formulation
9) A systematic approach to model formulation is to first construct the objective function before
determining the decision variables.
Answer: FALSE
Diff: 1
Page Ref: Ch 2 review
Main Heading: Formulation and Computer Solution
Key words: formulation
10) In a linear programming model, a resource constraint is a problem constraint with a greaterthan-or-equal-to (≥) sign.
Answer: FALSE
Diff: 1
Page Ref: Ch 2 review
Main Heading: Formulation and Computer Solution
Key words: formulation
11) Determining the production quantities of different products manufactured by a company
based on resource constraints is a product mix linear programming problem.
Answer: TRUE
Diff: 2
Page Ref: 111-116
Main Heading: A Product Mix Example
Key words: formulation, product mix problem
12) Product mix problems cannot have "greater than or equal to" (≥) constraints.
Answer: FALSE
Diff: 2
Page Ref: 111-116
Main Heading: A Product Mix Example
Key words: product mix
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13) When using a linear programming model to solve the "diet" problem, the objective is
generally to maximize profit.
Answer: FALSE
Diff: 2
Page Ref: 116-119
Main Heading: A Diet Example
Key words: objective function
14) When using a linear programming model to solve the "diet" problem, the objective is
generally to maximize nutritional content.
Answer: FALSE
Diff: 2
Page Ref: 116-119
Main Heading: A Diet Example
Key words: objective function
15) In formulating a typical diet problem using a linear programming model, we would expect
most of the constraints to be related to calories.
Answer: FALSE
Diff: 2
Page Ref: 116-119
Main Heading: A Diet Example
Key words: formulation, diet example
16) Solutions to diet problems in linear programming are always realistic.
Answer: FALSE
Diff: 2
Page Ref: 116-119
Main Heading: A Diet Example
Key words: diet example
17) Diet problems usually maximize nutritional value.
Answer: FALSE
Diff: 2
Page Ref: 116-119
Main Heading: A Diet Example
Key words: diet example
18) In most media selection decisions, the objective of the decision maker is to minimize cost.
Answer: FALSE
Diff: 2
Page Ref: 124-127
Main Heading: Marketing Example
Key words: marketing problem, media selection
19) In a media selection problem, instead of having an objective of maximizing profit or
minimizing cost, generally the objective is to maximize the audience exposure.
Answer: TRUE
Diff: 2
Page Ref: 124-127
Main Heading: Marketing Example
Key words: marketing problem, media selection
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20) Linear programming model of a media selection problem is used to determine the relative
value of each advertising media.
Answer: FALSE
Diff: 3
Page Ref: 124-127
Main Heading: Marketing Example
Key words: marketing problem, media selection
21) In a media selection problem, maximization of audience exposure may not result in
maximization of total profit.
Answer: TRUE
Diff: 2
Page Ref: 124-127
Main Heading: Marketing Example
Key words: marketing problem, media selection
22) In a balanced transportation model, supply equals demand such that all constraints can be
treated as equalities.
Answer: TRUE
Diff: 2
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: transportation problem, formulation
23) In an unbalanced transportation model, supply does not equal demand and supply constraints
have ≤ signs.
Answer: TRUE
Diff: 2
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: transportation problem, formulation
24) Transportation problems can have solution values that are non-integer and must be rounded.
Answer: FALSE
Diff: 3
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: transportation problem, solution
25) In a transportation problem, the supply constraint represents the maximum amount of
product available for shipment or distribution at a given source (plant, warehouse, mill).
Answer: TRUE
Diff: 1
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: transportation problem, formulation
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26) In a transportation problem, a supply constraint (the maximum amount of product available
for shipment or distribution at a given source) is a greater-than-or equal-to constraint (≥).
Answer: FALSE
Diff: 2
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: transportation problem, formulation
27) In a transportation problem, a demand constraint for a specific destination represents the
amount of product demanded by a given destination (customer, retail outlet, store).
Answer: TRUE
Diff: 2
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: transportation problem, formulation
28) In a transportation problem, a demand constraint (the amount of product demanded at a given
destination) is a less-than-or equal-to constraint (≤).
Answer: FALSE
Diff: 2
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: transportation problem, formulation
29) Blending problems usually require algebraic manipulation in order to write the LP in
"standard form."
Answer: TRUE
Diff: 1
Page Ref: 131-140
Main Heading: Data Envelopment Analysis
Key words: blending
30) Data Envelopment Analysis indicates which type of service unit makes the highest profit.
Answer: FALSE
Diff: 1
Page Ref: 140-144
Main Heading: A Blend Example
Key words: blending
31) Data Envelopment Analysis indicates the the relative _________ of a service unit compared
with others.
Answer: efficiency or productivity
Diff: 2
Page Ref: 140-144
Main Heading: Data Envelopment Analysis
Key words: data envelopment analysis
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32) __________ types of linear programming problems often result in fractional relations
between variables which must be eliminated.
Answer: blending
Diff: 2
Page Ref: 131-136
Main Heading: A Blend Example
Key words: blending
33) When formulating a linear programming model on a spreadsheet, the measure of
performance is located in the __________ cell.
Answer: target
Diff: 2
Page Ref: 113
Main Heading: Formulation and Computer Solution
Key words: spreadsheet solution
34) When the __________ command is used in an Excel spreadsheet, all the values in a column
(or row) are multiplied by the values in another column (or row) and then summed.
Answer: SUMPRODUCT
Diff: 2
Page Ref: 117
Main Heading: Formulation and Computer Solution
Key words: spreadsheet solution
35) For product mix problems, the constraints are usually associated with __________.
Answer: resources or time
Diff: 2
Page Ref: 111-116
Main Heading: A Product Mix Example
Key words: product mix
36) The __________ for the computer solution of a linear programming problem requires all
variables on the left side, and all numerical values on the right side of the inequality or equality
sign.
Answer: standard form
Diff: 2
Page Ref: 111-116
Main Heading: A Product Mix Example
Key words: formulation, constraint
37) The objective function of a diet problem is usually to __________ subject to nutritional
requirements.
Answer: minimize costs
Diff: 1
Page Ref: 116-119
Main Heading: A Diet Example
Key words: diet problem
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38) Investment problems maximize __________.
Answer: return on investments
Diff: 1
Page Ref: 119-124
Main Heading: An Investment Example
Key words: investment
39) In a media selection problem, instead of having an objective of maximizing profit or
minimizing cost, generally the objective is to maximize the __________.
Answer: audience exposure
Diff: 2
Page Ref: 124-127
Main Heading: Marketing Example
Key words: marketing problem, media selection
40) In __________ problem, maximization of audience exposure may not result in maximization
of total profit.
Answer: media selection
Diff: 3
Page Ref: 124-127
Main Heading: Marketing Example
Key words: marketing problem, media selection
41) In a balanced transportation model, supply equals __________ .
Answer: demand
Diff: 2
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: transportation problem, formulation
42) In a __________ transportation problem, supply exceeds demand.
Answer: unbalanced
Diff: 2
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: transportation problem, formulation
The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited
amount of the 3 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.
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43) What is the formulation for this problem?
Answer: MAX Z = 0. 4L + 0.5V
s.t.
2L + 3V ≤ 4800
6L + 8V ≤ 9600
1L + 2V ≤ 2000
Diff: 1
Page Ref: 111-116
Main Heading: Product Mix Example
Key words: computer solution
44) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which
resource is not completely used up and how much is remaining?
Answer: salt only, 1400 ounces remaining
Diff: 1
Page Ref: 111-116
Main Heading: A Product Mix Example
Key words: slack, computer solution
45) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which
resource is not completely used up and how much is remaining?
Answer: salt only, 1400 ounces remaining
Diff: 1
Page Ref: 111-116
Main Heading: A Product Mix Example
Key words: slack, computer solution
A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear
claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS (tablespoons) 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. The shop must produce at least 400 almond filled croissants
due to customer demand. Bear claw profits are 20 cents each, and almond-filled croissant profits
are 30 cents each.
46) This represents what type of linear programming application?
Answer: product mix
Diff: 1
Page Ref: 111-116
Main Heading: Product Mix Example
Key words: computer solution
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47) What is the formulation for this problem?
Answer: MAX Z = $.20B + $.30C
s.t.
6B + 3C ≤ 6600
1B + 1C ≤ 1400
2B + 4C ≤ 4800
C ≥ 400
Diff: 1
Page Ref: 111-116
Main Heading: Product Mix Example
Key words: formulation, constraint
48) For the production combination of 600 bear claws and 800 almond filled croissants, how
much flour and almond paste is remaining?
Answer: flour = 0 ounces and almond paste = 0 ounces
Diff: 1
Page Ref: 111-116
Main Heading: A Product Mix Example
Key words: slack, computer solution
49) If Xij = the production of product i in period j, write an expression to indicate that the limit
on production of the company's 3 products in period 2 is equal to 400.
Answer: X12 + X22 + X32 ≤ 400
Diff: 2
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: transportation problem, supply constraint
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50) Small motors for garden equipment is produced at 4 manufacturing facilities and needs to be
shipped to 3 plants that produce different garden items (lawn mowers, rototillers, leaf blowers).
The company wants to minimize the cost of transporting items between the facilities, taking into
account the demand at the 3 different plants, and the supply at each manufacturing site. The table
below shows the cost to ship one unit between each manufacturing facility and each plant, as
well as the demand at each plant and the supply at each manufacturing facility.
Write the formulation for this problem.
Answer: MIN Z = 4x1A + 4.5x1B + 3.2x1C + 3.5x2A + 3x2B +4x2C + 4x3A + 3.5x3B +
4.25x3C
s.t.
x1A + x1B +x1C = 200
x2A + x2B +x2C = 200
x3A + x3B +x3C = 300
x1A + x2A +x3A = 250
x1B + x2B +x3B = 150
x1C + x2C +x3C = 200
Diff: 2
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: computer solution, transportation/distribution
51) Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per
gallon on its water-base paint. Both paints contain two ingredients, A and B. 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. The company wishes to use linear
programming to determine the appropriate mix of oil-base and water-base paint to produce to
maximize its total profit. How much oil based and water based paint should the Quickbrush
make?
Answer: 9167 gallons of water based paint and 5833 gallons of oil based paint
Diff: 2
Page Ref: 131-136
Main Heading: A Blend Example
Key words: blending
10
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Andy Tyre manages Tyre's Wheels, Inc. Andy has received an order for 1000 standard wheels
and 1200 deluxe wheels next month, and for 750 standard wheels and 1000 deluxe wheels the
following months. He must fill all the orders. The cost of regular time production for standard
wheels is $25 and for deluxe wheels, $40. Overtime production costs 50% more. For each of the
next two months there are 1000 hours of regular time production and 500 hours of overtime
production available. A standard wheel requires .5 hours of production time and a deluxe wheel,
.6 hours. The cost of carrying a wheel from one month to the next is $2.
52) Define the decision variables and objective function for this problem.
Answer: Define the decision variables:
S1R = number of standard wheels produced in month 1 on regular time production
S1O = number of standard wheels produced in month 1 on overtime production
S2R = number of standard wheels produced in month 2 on regular time production
S2O = number of standard wheels produced in month 2 on overtime production
D1R = number of deluxe wheels produced in month 1 on regular time production
D1O = number of deluxe wheels produced in month 1 on overtime production
D2R = number of deluxe wheels produced in month 2 on regular time production
D2O = number of deluxe wheels produced in month 2 on overtime production
Y1 = number of standard wheels stored from month 1 to month 2.
Y2 = number of deluxe wheel s stored from month 1 to month 2.
MIN 25 S1R + 37.5 S1O +40 D1R + 60 D1O + 25 S2R + 37.5 S2O +40 D2R + 60 D2O +2 Y1
+2 Y2
Diff: 2
Page Ref: 136-145
Main Heading: Multiperiod Scheduling
Key words: linear program multiperiod scheduling
53) Write the constraints for this problem.
Answer: S1R + S1O - Y1 = 1000
.5 S1R + .6 D1R ≤ 1000
D1R + D1O - Y2 = 1200
.5 S1O + .6 D1O ≤ 500
S2R + S2O + Y1 = 750
.5 S2R + .6 D2R ≤ 1000
D2R + D2O + Y2 = 1000
.5 S2O + .6 D12O ≤ 50
Diff: 2
Page Ref: 136-145
Main Heading: Multiperiod Scheduling
Key words: linear program multiperiod scheduling
11
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Bullseye Shirt Company makes three types of shirts: Athletic, Varsity, and Surfer. The shirts
are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and
the cost for rayon is $7. Bullseye can receive up to 4,000 yards of cotton and 3,000 yards of
rayon per week.
The table below shows relevant manufacturing information:
Minimum
Total Yards of Fabric
weekly
Maximum
Shirt
fabric per shirt requirement contracts
Demand
at least 60%
Athletic
1.00
cotton
500
600
no more than
Varsity
1.20
30% rayon
650
850
As much as
Surfer
0.90
80% cotton 300
700
Selling Price
$30
$40
$36
54) Assume that the decision variables are defined as follows:
A = total number of athletic shirts produced
V = total number of varsity shirts produced
S = total number of surfer shirts produced
C = yards of cotton purchased
R = yards of rayon purchased
Xij = yards of fabric i (C or R) blended into shirt J (A, V or S)
Write the objective function.
Answer: max 30 A + 40 V + 36 S - 5C - 7R
Diff: 2
Page Ref: 131-136
Main Heading: A Blend Example
Key words: objective function, model construction
55) Write the constraints for the fabric requirements.
Answer: Form of constraints: Total yards used is greater than (or less than) total yards required
x (% fabric required) shirts produced
XCA≥ 0.6 A
XVR ≤0.36V
XSC≤ 0.72 S
Diff: 2
Page Ref: 131-136
Main Heading: A Blend Example
Key words: blending
12
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56) Write the constraints for the total number of shirts of each style produced.
Answer: Form of constraint: number of shirts produced = (total yards used to make the
shirt)/(yards/shirt)
A =( XCA + XRA)/1
V =( XCV + XRV)/1.2
S =( XCS + XRS)/0.9
Standard form:
A -XCA - XRA) = 0
1.2 V - XCV - XRV =0
0.9 S - XCS - XRS=0
Diff: 3
Page Ref: 131-136
Main Heading: A Blend Example
Key words: blending
57) 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:
Kitty 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 cost of this plan, and how much fat and protein do the cats
receive?
Answer: Cost is $3.50, which uses 16 cans of meow munch and 2 cans of feline fodder.
Diff: 2
Page Ref: 116-119
Main Heading: A Diet Example
Key words: diet
13
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58) A credit union wants to make investments in the following:
The firm will have $2,500,000 available for investment during the coming year. The following
restrictions apply:
∙ Risk free securities may not exceed 30% of the total funds, but must comprise at least 5% of the
total.
∙ Signature loans may not exceed 12% of the funds invested in all loans (vehicle, consumer, other
secured loans, and signature loans)
∙ Consumer loans plus other secured loans may not exceed the vehicle loans
∙ Other secured loans plus signature loans may not exceed the funds invested in risk free
securities. How should the $2,500,000 be allocated to each alternative to maximize annual
return? What is the annual return?
Answer:
Diff: 3
Page Ref: 119-124
Main Heading: Investment Example
Key words: investment
59) When systematically formulating a linear program, the first step is
A) Construct the objective function
B) Formulate the constraints
C) Identify the decision variables
D) Identify the parameter values
E) Identify a feasible solution
Answer: C
Diff: 2
Page Ref: 112
Main Heading: Formulation
Key words: formulation
14
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60) The following types of constraints are ones that might be found in linear programming
formulations:
1. ≤
2. =
3. >
A) 1 and 2
B) 2 and 3
C) 1 and 3
D) all of the above
Answer: A
Diff: 2
Page Ref: Review
Main Heading: A Product Mix Example
Key words: formulation, constraint
61) 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 two". The constraint for this
requirement can be written as:
A) x2 ≥ .60
B) x2 ≥ .60 (x2 + x7 + x8)
C) .4x2 - .6x7 - .6x8 ≤ 0
D) .4x2 - .6x7 - .6x8 ≥ 0
E) -.4x2 + .6x7 + .6x8 ≤ 0
Answer: C
Diff: 3
Page Ref: 119-124
Main Heading: An Investment Example
Key words: formulation
15
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62) 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
1
2
3
4
5
Percent per
pound in Feed A
20
30
0
24
10
Percent per
pound in Feed B
24
10
30
15
20
Minimum daily
requirement
(pounds)
30
50
20
60
40
The constraint for ingredient 3 is:
A) .5A + .75B = 20
B) .3B = 20
C) .3 B≤ 20
D) .3B ≥ 20
E) A + B = .3(20)
Answer: D
Diff: 2
Page Ref: 116-119
Main Heading: A Diet Example
Key words: solution
The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited
amount of the 3 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.
63) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which of the
three resources is (are) not completely used?
A) flour only
B) salt only
C) herbs only
D) salt and flour
E) salt and herbs
Answer: B
Diff: 2
Page Ref: 111-116
Main Heading: Product Mix Example
Key words: solution, slack
16
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64) What is the constraint for salt?
A) 6L + 8V ≤ 4800
B) 1L + 2V ≤ 4800
C) 3L + 2V ≤ 4800
D) 2L + 3V ≤ 4800
E) 2L + 1V ≤ 4800
Answer: D
Diff: 2
Page Ref: 111-116
Main Heading: Product Mix Example
Key words: formulation, constraint
65) Which of the following is not a feasible production combination?
A) 0L and 0V
B) 0L and 1000V
C) 1000L and 0V
D) 0L and 1200V
Answer: D
Diff: 1
Page Ref: 111-116
Main Heading: Product Mix Example
Key words: formulation, feasibility
66) 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,
A) X32 ≤ 400
B) X21 + X22 + X23 ≤ 400
C) X12 + X22 + X32 ≤ 400
D) X12 + X22 + X32 ≥ 400
E) X23 ≤ 400
Answer: C
Diff: 2
Page Ref: 111-116
Main Heading: Product Mix Example
Key words: formulation, constraint
67) Balanced transportation problems have the following type of constraints:
A) ≥
B) ≤
C) =
D) <
E) None of the above
Answer: C
Diff: 2
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: formulation, constraint
17
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68) Compared to blending and product mix problems, transportation problems are unique
because
A) They maximize profit.
B) The constraints are all equality constraints with no "≤" or "≥" constraints.
C) They contain fewer variables.
D) The solution values are always integers.
E) All of the above are True.
Answer: D
Diff: 2
Page Ref: 127-131
Main Heading: A Transportation Example
Key words: transportation
69) The production manager for the Softy soft drink company is considering the production of 2
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?
A) 2R + 4D ≤ 480
B) 2D + 4R ≤ 480
C) 2R + 3D ≤ 480
D) 3R + 2D ≤ 480
E) 3R + 4D ≤ 480
Answer: A
Diff: 2
Page Ref: 131-136
Main Heading: A Blend Example
Key words: formulation, constraint
70) A croissant shop produces 2 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?
A) $380
B) $400
C) $420
D) $440
E) $480
Answer: A
Diff: 2
Page Ref: 131-136
Main Heading: A Blend Example
Key words: computer solution
18
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71) The production manager for the Softy soft drink company is considering the production of 2
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 her ingredient) 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?
A) $220
B) $270
C) $320
D) $420
E) $520
Answer: D
Diff: 2
Page Ref: 131-136
Main Heading: A Blend Example
Key words: computer solution
72) 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.
A) x21 + x22 ≤ 8000
B) x12 + x22 ≥ 8000
C) x11 + x12 ≤ 8000
D) x21 + x22 ≥ 8000
E) x11 + x12 ≥ 8000
Answer: C
Diff: 2
Page Ref: 131-136
Main Heading: A Blend Example
Key words: formulation
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73) 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 demand constraint
for gasoline type 1.
A) x21 + x22 = 11000
B) x12 + x22 = 11000
C) x11 + x21 ≤ 11000
D) x11 + x21 = 11000
E) x11 + x12 ≥ 11000
Answer: D
Diff: 2
Page Ref: 131-136
Main Heading: A Blend Example
Key words: formulation
74) 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 constraint stating
that the component 1 cannot account for more than 35% of the gasoline type 1.
A) x11 + x12 (.35)(x11 + x21)
B) x11 .35 (x11 + x21)
C) x11 .35 (x11 + x12)
D) -.65x11 + .35x21 ≤ 0
E) .65x11 - .35x21 ≤ 0
Answer: E
Diff: 3
Page Ref: 131-136
Main Heading: A Blend Example
Key words: formulation
20
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
75) 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 based and water based
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 based paint, and y represents the gallons of water
based paint, which constraint is correctly represents the constraint on ingredient A?
A) .9A + .1B ≤ 10,000
B) .9x + .1y ≤ 10,000
C) .3x + .7y ≤ 10,000
D) .9x + .3y ≤ 10,000
E) .1x + .9y ≤ 10,000
Answer: D
Diff: 2
Page Ref: 131-136
Main Heading: A Blend Example
Key words: blend
76) A systematic approach to model formulation is to first
A) construct the objective function
B) develop each constraint separately
C) define decision variables
D) determine the right hand side of each constraint
E) all of the above
Answer: C
Diff: 2
Page Ref: 112
Main Heading: A Multiperiod Scheduling Example
Key words: model formulation
77) Let: rj = regular production quantity for period j, oj =overtime production quantity in period
j, ii = inventory quantity in period j, and di = demand quantity in period j Correct formulation of
the demand constraint for a multi-period scheduling problem is:
A) rj + oj + i2 - i1 ≥ di
B) rj + oj + i1 - i2 ≥ di
C) rj + oj + i1 - i2 ≤ di
D) rj - oj - i1 + i2 ≥ di
E) rj + oj + i2 - i1 ≤ di
Answer: A
Diff: 2
Page Ref: 136-140
Main Heading: A Multiperiod Scheduling Example
Key words: formulation, constraint
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78) In a multi-period scheduling problem the production constraint usually takes the form of:
A) beginning inventory + demand - production = ending inventory
B) beginning inventory - demand + production = ending inventory
C) beginning inventory - ending inventory + demand = production
D) beginning inventory - production - ending inventory = demand
E) beginning inventory + demand + production = ending inventory
Answer: B
Diff: 2
Page Ref: 136-140
Main Heading: A Multiperiod Scheduling Example
Key words: model formulation, multi-period scheduling problem
79) The type of linear program that compares services to indicate which one is less productive or
inefficient is called
A) product mix
B) data envelopment analysis
C) marketing
D) blending
E) multi period scheduling
Answer: B
Diff: 2
Page Ref: 140
Main Heading: Data Envelopment Analysis
Key words: formulation
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.
80) 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 formulate as a linear programming constraint?
A) X2 ≤ 10000
X2 + X3 ≤350
B) 10,000 X2 ≤ 350X2 + 350X3
C) 47.25X2 ≤10,000
X2 + X3 ≤ 350
D) 47.25X2 ≤10,000
47.25 X2 + 110X3 ≤ 350
Answer: C
Diff: 2
Page Ref: 119-124
Main Heading: An Investment Example
Key words: investment
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81) An appropriate part of the model would be
A) 15X1 + 47.25X2 +110 X3 ≤ 50,000
B) MAX 15X1 + 47.25X2 + 110X3
C) X1 + X2 +X3 ≤ 50,000
D) MAX 50(15)X1 + 50 (47.25)X2 + 50 (110)X3
Answer: A
Diff: 2
Page Ref: 119-124
Main Heading: An Investment Example
Key words: investment
82) The expected returns on investment of the three stocks are 6%, 8%, and 11%. An
appropriate objective function is
A) MAX .06X1 +.08X2 +.11X3
B) MAX .06(15)X1 +.08(47.25)X2 +.11(110)X3
C) MAX 15X1 + 47.25X2 +.110X3
D) MAX (1/.06)X1 +.(1/08)X2 + (1/.11)X3
Answer: B
Diff: 2
Page Ref: 119-124
Main Heading: An Investment Example
Key words: investment
83) The investor stipulates that stock 1 must not account for more than 35% of the number of
shares purchased. Which constraint is correct?
A) X1 ≤ 0.35
B) X1 = 0.35 (50000)
C) X1 ≤ 0.35(X1 + X2 +.X3)
D) X1 = 0.35(X1 + X2 +.X3)
Answer: C
Diff: 2
Page Ref: 119-124
Main Heading: An Investment Example
Key words: investment
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