Chapter 1 – Introduction
True / False
1. The process of decision making is more limited than that of problem solving.
a.
True
b.
False
True
1
Problem solving and decision making
2. The terms ‘stochastic’ and ‘deterministic’ have the same meaning in quantitative analysis.
a.
True
b.
False
3. The volume that results in marginal revenue equaling marginal cost is called the break-even point.
a.
True
b.
False
False
1
Problem solving and decision making
4. Problem solving encompasses both the identification of a problem and the action to resolve it.
a.
True
b.
False
True
1
Problem solving and decision making
5. The decision making process includes implementation and evaluation of the decision.
a.
True
b.
False
False
1
Problem solving and decision making
6. The most successful quantitative analysis will separate the analyst from the managerial team until after the problem is
fully structured.
a.
True
b.
False
False
1
Quantitative analysis
7. The value of any model is that it enables the user to make inferences about the real situation.
Chapter 1 – Introduction
a.
True
b.
False
8. Uncontrollable inputs are the decision variables for a model.
a.
True
b.
False
9. The feasible solution is the best solution possible for a mathematical model.
a.
True
b.
False
False
1
10. A company seeks to maximize profit subject to limited availability of man-hours. Man-hours is a controllable input.
a.
True
b.
False
11. Frederick Taylor is credited with forming the first MS/OR interdisciplinary teams in the 1940’s.
a.
True
b.
False
False
1
Introduction
12. To find the choice that provides the highest profit and the fewest employees, apply a single-criterion decision process.
a.
True
b.
False
False
1
13. The most critical component in determining the success or failure of any quantitative approach to decision making is
problem definition.
a.
True
b.
False
Chapter 1 – Introduction
True
1
14. The first step in the decision making process is to identify the problem.
a.
True
b.
False
True
1
Introduction
15. All uncontrollable inputs or data must be specified before we can analyze the model and recommend a decision or
solution for the problem.
a.
True
b.
False
True
1
16. In quantitative analysis, the optimal solution is the mathematically-best solution.
a.
True
b.
False
True
1
17. If you are deciding to buy either machine A, B, or C with the objective of minimizing the sum of labor, material and
utility costs, you are dealing with a single-criterion decision.
a.
True
b.
False
True
1
18. Model development should be left to quantitative analysts; the model user’s involvement should begin at the
implementation stage.
a.
True
b.
False
False
1
19. A feasible solution is one that satisfies at least one of the constraints in the problem.
a.
True
b.
False
False
20. A toy train layout designed to represent an actual railyard is an example of an analog model.
a.
True
b.
False
Multiple Choice
21. The field of management science
a.
approaches decision making rationally, with techniques based on the scientific method.
b.
concentrates on the use of quantitative methods to assist in decision making.
c.
is another name for decision science and for operations research.
d.
each of these choices are true.
d
1
Introduction
22. Identification and definition of a problem
a.
is the final step of problem solving.
b.
cannot be done until alternatives are proposed.
c.
requires consideration of multiple criteria.
d.
is the first step of decision making.
d
1
Problem solving and decision making
23. Decision alternatives
a.
should be identified before decision criteria are established.
b.
are limited to quantitative solutions
c.
are evaluated as a part of the problem definition stage.
d.
are best generated by brain-storming.
a
1
Problem solving and decision making
24. Decision criteria
a.
are the ways to evaluate the choices faced by the decision maker.
b.
are the choices faced by the decision maker.
c.
must be unique for a problem.
d.
are the problems faced by the decision maker.
a
1
Model solution
Chapter 1 – Introduction
25. In a multicriteria decision problem
a.
successive decisions must be made over time.
b.
it is impossible to select a single decision alternative.
c.
the decision maker must evaluate each alternative with respect to each criterion.
d.
each of these choices are true.
c
1
Problem solving and decision making
26. The quantitative analysis approach requires
a.
mathematical expressions for the relationships.
b.
the manager’s prior experience with a similar problem.
c.
a relatively uncomplicated problem.
a
1
Quantitative analysis and decision making
27. A physical model that does not have the same physical appearance as the object being modeled is
a.
a qualitative model.
b.
a mathematical model.
c.
an analog model.
d.
an iconic model.
28. Inputs to a quantitative model
a.
must all be deterministic if the problem is to have a solution.
b.
are uncertain for a stochastic model.
c.
are a trivial part of the problem solving process.
d.
are uncontrollable for the decision variables.
29. When the value of the output cannot be determined even if the value of the controllable input is known, the model is
a.
deterministic.
b.
analog.
c.
stochastic.
d.
digital.
1
Problem solving and decision making
Chapter 1 – Introduction
30. The volume that results in total revenue being equal to total cost is the
a.
profit mix.
b.
marginal volume.
c.
marginal cost.
d.
break-even point.
d
1
Break-even analysis
31. Management science and operations research both involve
a.
operational management skills.
b.
quantitative approaches to decision making.
c.
scientific research as opposed to applications.
d.
qualitative managerial skills.
b
1
Introduction
32. George Dantzig is important in the history of management science because he developed
a.
the scientific management revolution.
b.
powerful digital computers.
c.
World War II operations research teams.
d.
the simplex method for linear programming.
d
1
Introduction
33. The first step in problem solving is
a.
definition of decision variables.
b.
the identification of a difference between the actual and desired state of affairs.
c.
determination of the correct analytical solution procedure.
d.
implementation.
b
1
Problem solving and decision making
34. Problem definition
a.
must involve the analyst and the user of the results.
b.
includes specific objectives and operating constraints.
c.
must occur prior to the quantitative analysis process.
d.
each of these choices are true.
d
1
Model development
Chapter 1 – Introduction
35. A model that uses a system of symbols to represent a problem is called
a.
iconic.
b.
constrained.
c.
mathematical.
d.
analog.
36. Which of the following is not one of the commonly used names for the body of knowledge involving quantitative
approaches to decision-making?
a.
efficiency studies
b.
management science
c.
business analytics
d.
operations research
a
1
Introduction
Subjective Short Answer
37. A snack food manufacturer buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The
price per unit of the Iowa corn is $6.00 and the price per unit of the Illinois corn is $5.50.
a.
Define variables that would tell how many units to purchase from each source.
b.
Develop an objective function that would minimize the total cost.
c.
The manufacturer needs at least 12000 units of corn. The Iowa cooperative can supply up to
8000 units, and the Illinois cooperative can supply at least 6000 units. Develop constraints
for these conditions.
1
Model development
38. The relationship d = 5000 − 25p describes what happens to demand (d) as price (p) varies. Here, price can vary
between $10 and $50.
a.
How many units can be sold at the $10 price? How many can be sold at the $50 price?
b.
Model the expression for total revenue.
c.
Consider prices of $20, $30, and $40. Which of these three price alternative will maximize
total revenue? What are the values for demand and revenue at this price?
Quantitative analysis
Chapter 1 – Introduction
a.
For p = 10, d = 4750
For p = 50, d = 3750
b.
c.
For p = 20, d = 4500, TR = $90,000
For p = 30, d = 4250, TR = $127,500
For p = 40, d = 4000, TR = $160,000 (maximum total revenue)
1
Model development
39. There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is
$25. The revenue per unit is projected to be $45.
a.
Write an expression for total cost.
b.
Write an expression for total revenue.
c.
Write an expression for total profit.
d.
Find the break-even point.
a.
C(x) = 50000 + 25x
b.
R(x) = 45x
c.
P(x) = 45x − (50000 + 25x)
d.
x = 2500
1
Break-even analysis
40. An author has received an advance against royalties of $10,000. The royalty rate is $1.00 for every book sold in the
United States, and $1.35 for every book sold outside the United States. Define variables for this problem and write an
expression that could be used to calculate the number of books to be sold to cover the advance.
1
Break-even analysis
41. A university schedules summer school courses based on anticipated enrollment. The cost for faculty compensation,
laboratories, student services, and allocated overhead for a computer class is $8500. If students pay $920 to enroll in the
course, how large would enrollment have to be for the university to break even?
Enrollment would need to be 10 students.
1
Break-even analysis
42. As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast
operation, the prospective owners have projected:
Monthly fixed cost (loan payment, taxes, insurance, maintenance)
$6000
Variable cost per occupied room per night
$ 20
Revenue per occupied room per night
$ 75
a.
Write the expression for total cost per month. Assume 30 days per month.
b.
Write the expression for total revenue per month.
c.
If there are 12 guest rooms available, can they break even? What percentage of rooms would
need to be occupied, on average, to break even?
Chapter 1 – Introduction
a.
C(x) = 6000 + 20(30)x (monthly)
b.
R(x) = 75(30)x (monthly)
break even. This would be a 33% occupancy rate.
1
Break-even analysis
43. Organizers of an Internet training session will charge participants $150 to attend. It costs $3000 to reserve the room,
hire the instructor, bring in the equipment, and advertise. Assume it costs $25 per student for the organizers to provide the
course materials.
a.
How many students would have to attend for the company to break even?
b.
If the trainers think, realistically, that 20 people will attend, then what price should be
charged per person for the organization to break even?
a.
C(x) = 3000 + 25x
R(x) = 150x
Break-even students = 24
b.
Cost = 3000 + 25(20)
Revenue = 20p
Break-even price = 175
1
Break-even analysis
44. In this portion of an Excel spreadsheet, the user has given values for selling price, the costs, and a sample volume.
Give the cell formula for
a.
cell E12, break-even volume.
b.
cell E16, total revenue.
c.
cell E17, total cost.
d.
cell E19, profit (loss).
A
B
C
D
E
1
2
3
4
Break-even calculation
5
6
Selling price per unit
10
7
8
Costs
9
Fix cost
8400
10
Variable cost per unit
4.5
11
12
Break-even volume
13
14
Sample calculation
15
Volume
2000
16
Total revenue
17
Total cost
18
19
Profit (loss)
Chapter 1 – Introduction
a.
=E9/(E6-E10)
b.
=E15*E6
c.
=E9+E10*E15
d.
=E16-E17
1
Spreadsheets for management science
45. A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each
chair utilizes 30 sq. ft. At least five sofas and at least five chairs are to be displayed.
a.
Write a mathematical model representing the store’s constraints.
b.
Suppose the profit on sofas is $200 and on chairs is $100. On a given day, the probability
that a displayed sofa will be sold is .03 and that a displayed chair will be sold is .05.
Mathematically model each of the following objectives:
1.
Maximize the total pieces of furniture displayed.
2.
Maximize the total expected number of daily sales.
3.
Maximize the total expected daily profit.
a.
50s + 30c ≤ 800
s ≥ 5
c ≥ 5
b.
(1) Max s + c
(2) Max .03s + .05c
(3) Max 6s + 5c
1
Model development
46. A manufacturer makes two products, doors and windows. Each must be processed through two work areas. Work area
#1 has 60 hours of available production time per week. Work area #2 has 48 hours of available production time per week.
Manufacturing of a door requires 4 hours in work area #1 and 2 hours in work area #2. Manufacturing of a window
requires 2 hours in work area #1 and 4 hours in work area #2. Profit is $8 per door and $6 per window.
a.
Define decision variables that will tell how many units to build (doors and windows) per
week.
b.
Develop an objective function that will maximize total profit per week.
c.
Develop production constraints for work area #1 and #2.
a.
Let D = the number of doors to build per week
Let N = the number of windows to build per week
b.
Weekly Profit = 8D + 6W
c.
4D + 2W ≤ 60
2D + 4W ≤ 48
1
Model development
47. A small firm builds galvanized swing sets. The investment in plant and equipment is $200,000. The variable cost per
swing set is $500. The selling price of the swing set is $1000. How many swing sets would have to be sold for the firm to
break even?
400 swing sets
1
Break-even analysis
Chapter 1 – Introduction
48. A computer rework center has the capacity to rework 300 computers per day. The expected number of computers
needing to be reworked per day is 225. The center is paid $26 for each computer reworked. The fixed cost of renting the
reworking equipment is $250 per day. Work space rents for $150 per day. The cost of material is $18 per computer and
labor costs $3 per computer. What is the break-even number of computers reworked per day?
80 computers
Break-even analysis
49. To establish a driver education school, organizers must decide how many cars, instructors, and students to have. Costs
are estimated as follows. Annual fixed costs to operate the school are $30,000. The annual cost per car is $3000. The
annual cost per instructor is $11,000 and one instructor is needed for each car. Tuition for each student is $350. Let x be
the number of cars and y be the number of students.
a.
Write an expression for total cost.
b.
Write an expression for total revenue.
c.
Write an expression for total profit.
d.
The school offers the course eight times each year. Each time the course is offered, there are
two sessions. If they decide to operate five cars, and if four students can be assigned to each
car, will they break even?
a.
C(x) = 30000 + 14000x
b.
R(y) = 350y
c.
P(x,y) = 350y − (30000 + 14000x)
five cars is 350(320) − (30000 + 14000(5)) = 12000. So, the school can reach the break-even
1
Break-even analysis
50. Zipco Printing operates a shop that has five printing machines. The machines differ in their capacities to perform
various printing operations due to differences in the machines’ designs and operator skill levels. At the start of the
workday there are five printing jobs to schedule. The manager must decide what the job-machine assignments should be.
a.
How could a quantitative approach to decision making be used to solve this problem?
b.
What would be the uncontrollable inputs for which data must be collected?
c.
Define the decision variables, objective function, and constraints to appear in the
mathematical model.
d.
Is the model deterministic or stochastic?
e.
Suggest some simplifying assumptions for this problem.
a.
A quantitative approach to decision making can provide a systematic way for deciding the
job-machine pairings so that total job processing time is minimized.
How long it takes to process each job on each machine, and any job-machine pairings that
are unacceptable.
c.
Decision variables: one for each job-machine pairing, taking on a value of 1 if the pairing is
used and 0 otherwise.
Objective function: minimize total job processing time.
Constraints: each job is assigned to exactly one machine, and each machine be assigned no
more than one job.
performance, and more.
e.
Assume that processing times are deterministic (known/fixed).
1
Chapter 1 – Introduction
TOPICS:
Model development
51. Consider a department store that must make weekly shipments of a certain product from two different warehouses to
four different stores.
a.
How could a quantitative approach to decision making be used to solve this problem?
b.
What would be the uncontrollable inputs for which data must be gathered?
c.
What would be the decision variables of the mathematical model? the objective function? the
constraints?
d.
Is the model deterministic or stochastic?
e.
Suggest assumptions that could be made to simplify the model.
A quantitative approach to decision making can provide a systematic way to determine a
minimum shipping cost from the warehouses to the stores.
Fixed costs and variable shipping costs; the demand each week at each store; the supplies
each week at each warehouse.
exceeding the supplies at the warehouses.
depending upon the amount shipped, other goods sent with a shipment, etc.
e.
Make the model deterministic by assuming fixed shipping costs per item, demand is constant
at each store each week, and weekly supplies in the warehouses are constant.
POINTS:
1
TOPICS:
Model development
52. Three production processes – A, B, and C – have the following cost structure:
Process
Fixed Cost
per Year
Variable Cost
per Unit
A
$120,000
$3.00
B
90,000
4.00
C
80,000
4.50
a.
What is the most economical process for a volume of 8,000 units?
b.
How many units per year must be sold with each process to have annual profits of $50,000 if the selling price is $6.95
per unit?
c.
What is the break-even volume for each process?
c. At breakeven, profit (the pretax profits per period) is equal to zero.
Chapter 1 – Introduction
53. Jane Persico, facility engineer at the El Paso plant of Computer Products Corporation (CPC), is studying a process
selection decision at the plant. A new printer is to be manufactured and she must decide whether the printer will be auto–
assembled or manually assembled. The decision is complicated by the fact that annual production volume is expected to
increase by almost 50% over three years. Jane has developed these estimates for two alternatives for the printer assembly
process:
Auto-
Assembly
Process
Manual
Assembly
Process
Annual fixed cost
$690,000
$269,000
Variable cost per product
$29.56
$31.69
Estimated annual production
(in number of products):
Year 1
152,000
152,000
Year 2
190,000
190,000
Year 3
225,000
225,000
a.
Which production process would be the least-cost alternative in Years 1, 2, and 3?
b.
How much would the variable cost per unit have to be in Year 2 for the auto-assembly process to justify the additional
annual fixed cost for the auto-assembly process over the manual assembly process?
Chapter 1 – Introduction
TOPICS:
Cost and volume models
Essay
54. Should the problem solving process be applied to all problems?
ANSWER:
Answer not provided.
POINTS:
1
TOPICS:
Problem solving and decision making
55. Explain the difference between quantitative and qualitative analysis from the manager’s point of view.
ANSWER:
Answer not provided.
POINTS:
1
TOPICS:
Quantitative analysis and decision making
56. Explain the relationship among model development, model accuracy, and the ability to obtain a solution from a model.
ANSWER:
Answer not provided.
POINTS:
1
TOPICS:
Model solution
57. What are three of the management science techniques that practitioners use most frequently? How can the
effectiveness of these applications be increased?
ANSWER:
Answer not provided.
POINTS:
1
TOPICS:
Methods used most frequently
58. What steps of the problem solving process are involved in decision making?
ANSWER:
Answer not provided.
POINTS:
1
TOPICS:
Introduction
59. Give three benefits of model development and an example of each.
ANSWER:
Answer not provided.
POINTS:
1
TOPICS:
Model development
60. Explain the relationship between information systems specialists and quantitative analysts in the solution of large
mathematical problems.
ANSWER:
Answer not provided.
POINTS:
1
TOPICS:
Data preparation
61. Define and contrast the terms feasible solution, infeasible solution and optimal solution.
ANSWER:
Answer not provided.
POINTS:
1
TOPICS:
Model solution
62. Define three forms of models and provide an example of each.
Chapter 1 – Introduction
63. Explain the difference between controllable and uncontrollable inputs to a mathematical model and provide an
example of each.