Chapter 1 – Introduction
True / False
1. The process of decision making is more limited than that of problem solving.
a. True
b. False
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
4. Problem solving encompasses both the identification of a problem and the action to resolve it.
a. True
b. False
5. The decision making process includes implementation and evaluation of the decision.
a. True
b. False
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
7. The value of any model is that it enables the user to make inferences about the real situation.
a. True
b. False
Chapter 1 – Introduction
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
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
12. To find the choice that provides the highest profit and the fewest employees, apply a single-criterion decision process.
a. True
b. False
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
14. The first step in the decision making process is to identify the problem.
Chapter 1 – Introduction
a. True
b. False
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
16. In quantitative analysis, the optimal solution is the mathematically-best solution.
a. True
b. False
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
18. Model development should be left to quantitative analysts; the model user’s involvement should begin at the
implementation stage.
a. True
b. False
19. A feasible solution is one that satisfies at least one of the constraints in the problem.
a. True
b. False
20. A toy train layout designed to represent an actual railyard is an example of an analog model.
a. True
b. False
Chapter 1 – Introduction
Multiple Choice
21. The field of management science
a. concentrates on the use of quantitative methods to assist in decision making.
b. approaches decision making rationally, with techniques based on the scientific method.
c. is another name for decision science and for operations research.
d. each of these choices are true.
22. Identification and definition of a problem
a. cannot be done until alternatives are proposed.
b. is the first step of decision making.
c. is the final step of problem solving.
d. requires consideration of multiple criteria.
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.
24. Decision criteria
a. are the choices faced by the decision maker.
b. are the problems faced by the decision maker.
c. are the ways to evaluate the choices faced by the decision maker.
d. must be unique for a problem.
25. In a multicriteria decision problem
a. it is impossible to select a single decision alternative.
b. the decision maker must evaluate each alternative with respect to each criterion.
c. successive decisions must be made over time.
d. each of these choices are true.
Chapter 1 – Introduction
26. The quantitative analysis approach requires
a. the manager’s prior experience with a similar problem.
b. a relatively uncomplicated problem.
c. mathematical expressions for the relationships.
27. A physical model that does not have the same physical appearance as the object being modeled is
a. an analog model.
b. an iconic model.
c. a mathematical model.
d. a qualitative model.
28. Inputs to a quantitative model
a. are a trivial part of the problem solving process.
b. are uncertain for a stochastic model.
c. are uncontrollable for the decision variables.
d. must all be deterministic if the problem is to have a solution.
29. When the value of the output cannot be determined even if the value of the controllable input is known, the model is
a. analog.
b. digital.
c. stochastic.
d. deterministic.
30. The volume that results in total revenue being equal to total cost is the
a. break-even point.
b. marginal volume.
c. marginal cost.
d. profit mix.
31. Management science and operations research both involve
a. qualitative managerial skills.
b. quantitative approaches to decision making.
c. operational management skills.
d. scientific research as opposed to applications.
Chapter 1 – Introduction
32. George Dantzig is important in the history of management science because he developed
a. the scientific management revolution.
b. World War II operations research teams.
c. the simplex method for linear programming.
d. powerful digital computers.
33. The first step in problem solving is
a. determination of the correct analytical solution procedure.
b. definition of decision variables.
c. the identification of a difference between the actual and desired state of affairs.
d. implementation.
34. Problem definition
a. includes specific objectives and operating constraints.
b. must occur prior to the quantitative analysis process.
c. must involve the analyst and the user of the results.
d. each of these choices are true.
35. A model that uses a system of symbols to represent a problem is called
a. mathematical.
b. iconic.
c. analog.
d. constrained.
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. management science
b. business analytics
c. operations research
d. efficiency studies
Chapter 1 – Introduction
37. The scientific management revolution of the early 1900s was initiated by
a. James Lingo
b. Herbert Simon
c. Frederic Taylor
d. George Dantzig
38. The decision variables of a model are also known as the
a. uncontrollable output
b. controllable inputs
c. environmental factors
d. projected results
39. A physical model that has the same physical appearance as the object being modeled is
a. an analog model
b. an iconic model
c. a mathematical model
d. a deterministic model
40. When production volume exceeds the breakeven point, we can expected
a. fixed cost to decrease
b. a loss
c. marginal revenue to decrease
d. a profit
Subjective Short Answer
41. 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.
Chapter 1 – Introduction
42. 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?
43. 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.
44. 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.
45. 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?
Chapter 1 – Introduction
46. 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?
47. 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?
48. 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
Chapter 1 – Introduction
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)
49. 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.
50. 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.
Chapter 1 – Introduction
51. 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?
52. 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?
53. 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
54. 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.
Chapter 1 – Introduction
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.
55. 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.
56. 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?
Chapter 1 – Introduction
57. 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
58. Janice Smith is an expert at calligraphy. However, it is found that a specialized robot can imitate Janice’s work
perfectly. Variable costs are 75% of selling price and fixed costs are $190,000 for the robot system.
a. How many pieces must be produced to break even assuming she sells each piece for $200?
b. How many pieces must be produced to break even if she sells them for $250 and variable costs drop to 70% of selling
price?
Essay
59. Should the problem solving process be applied to all problems?
60. Explain the difference between quantitative and qualitative analysis from the manager’s point of view.
61. Explain the relationship among model development, model accuracy, and the ability to obtain a solution from a model.
62. What are three of the management science techniques that practitioners use most frequently? How can the
effectiveness of these applications be increased?
Chapter 1 – Introduction
63. What steps of the problem solving process are involved in decision making?
64. Give three benefits of model development and an example of each.
65. Explain the relationship between information systems specialists and quantitative analysts in the solution of large
mathematical problems.
66. Define and contrast the terms feasible solution, infeasible solution and optimal solution.
67. Define three forms of models and provide an example of each.
68. Explain the difference between controllable and uncontrollable inputs to a mathematical model and provide an
example of each.