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Chapter 1 Introduction
University of California Los Angeles
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True / False
- The process of decision making is more limited than that of problem solving. a. True
b. Fals e
ANSWER: True
POINTS: 1
TOPICS: Problem solving and decision making
- The terms 'stochastic' and 'deterministic' have the same meaning in quantitative analysis. a. True
b. Fals e
ANSWER: False
POINTS: 1
TOPICS: Model development
- The volume that results in marginal revenue equaling marginal cost is called the break-even point. a. True
b. Fals e
ANSWER: False
POINTS: 1
TOPICS: Problem solving and decision making
- Problem solving encompasses both the identification of a problem and the action to resolve it. a. True
b. Fals e
ANSWER: True
POINTS: 1
TOPICS: Problem solving and decision making
- The decision making process includes implementation and evaluation of the decision. a. True
b. Fals e
ANSWER: False
POINTS: 1
TOPICS: Problem solving and decision making
- The most successful quantitative analysis will separate the analyst from the managerial team until after the problem is
fully structured. a. True
b. Fals e
ANSWER: False
POINTS: 1
TOPICS: Quantitative analysis
- The value of any model is that it enables the user to make inferences about the real situation. a. True
b. Fals e
ANSWER: True
POINTS: 1
TOPICS: Model development
- Uncontrollable inputs are the decision variables for a model. a. True
b. Fals e
ANSWER: False
POINTS: 1
TOPICS: Model development
- The feasible solution is the best solution possible for a mathematical model. a. True
b. Fals e
ANSWER: False
POINTS: 1
TOPICS: Model solution
- A company seeks to maximize profit subject to limited availability of man-hours. Man-hours is a controllable input. a. True
b. Fals e
ANSWER: False
POINTS: 1
TOPICS: Model development
- Frederick Taylor is credited with forming the first MS/OR interdisciplinary teams in the 1940's. a. True
b. Fals e
TOPICS: Quantitative analysis
- 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. Fals e
ANSWER: True
POINTS: 1
TOPICS: Problem solving and decision making
- Model development should be left to quantitative analysts; the model user's involvement should begin at the implementation stage. a. True
b. Fals e
ANSWER: False
POINTS: 1
TOPICS: Problem solving and decision making
- A feasible solution is one that satisfies at least one of the constraints in the problem. a. True
b. Fals e
ANSWER: False
POINTS: 1
TOPICS: Model solution
- A toy train layout designed to represent an actual railyard is an example of an analog model. a. True
b. Fals e
ANSWER: False
POINTS: 1
TOPICS: Model development
Multiple Choice
- 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.
ANSWER: d
POINTS: 1
TOPICS: Introduction
- 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.
ANSWER: b
POINTS: 1
TOPICS: Problem solving and decision making
- 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.
ANSWER: a
POINTS: 1
TOPICS: Problem solving and decision making
- 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.
ANSWER: c
POINTS: 1
TOPICS: Problem solving and decision making
- 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.
ANSWER: b
POINTS: 1
d. profit mix.
ANSWER: a
POINTS: 1
TOPICS: Break-even analysis
- 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.
ANSWER: b
POINTS: 1
TOPICS: Introduction
- 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.
ANSWER: c
POINTS: 1
TOPICS: Introduction
- 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.
ANSWER: c
POINTS: 1
TOPICS: Problem solving and decision making
- 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.
ANSWER: d
POINTS: 1
TOPICS: Quantitative analysis
- A model that uses a system of symbols to represent a problem is called a. mathematical .
b. iconic.
c. analog.
d. constrained.
ANSWER: a
POINTS: 1
TOPICS: Model development
- 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
ANSWER: d
POINTS: 1
TOPICS: Introduction
- The scientific management revolution of the early 1900s was initiated by a. James Lingo
b. Herbert Simon
c. Frederic Taylor
d. George Dantzig
ANSWER: c
POINTS: 1
- The decision variables of a model are also known as the a. uncontrollable output
b. controllable inputs
c. environmental factors
d. projected results
ANSWER: b
POINTS: 1
- 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
ANSWER: b
c. Write an expression for total profit. d. Find the break-even point. ANSWER : a. C(x) = 50000 + 25x b. R(x) = 45x c. P(x) = 45x − (50000 + 25x) d. x = 2500
POINTS: 1
TOPICS: Break-even analysis
- An author has received an advance against royalties of $10,000. The royalty rate is $1 for every book sold in the United States, and $1 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. ANSWER: Let x 1 = the number of books sold in the U.
Let x 2 = the number of books sold outside the U. 10000 = 1x 1 + 1 2
POINTS: 1
TOPICS: Break-even analysis
- 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? ANSWER: Enrollment would need to be 10 students.
POINTS: 1
TOPICS: Break-even analysis
- 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) $ 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? ANSWER : a. C(x) = 6000 + 20(30)x (monthly) b. R(x) = 75(30)x (monthly) c. Break-even occupancy = 3 or 4 occupied rooms per night, so they have enough rooms to break even. This would be a 33% occupancy rate.
POINTS: 1
TOPICS: Break-even analysis
- 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? ANSWER : a. C(x) = 3000 + 25x R(x) = 150x Break-even students = 24 b. Cost = 3000 + 25(20) Revenue = 20p Break-even price = 175
POINTS: 1
TOPICS: Break-even analysis
- 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. 11 12 Break-even volume 13 14 Sample calculation 15 Volume 2000 16 Total revenue 17 Total cost 18 19 Profit (loss)
ANSWER : a. =E9/(E6-E10) b. =E15E c. =E9+E10E d. =E16-E
POINTS: 1
TOPICS: Spreadsheets for management science
- 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
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? ANSWER : a. C(x) = 30000 + 14000x b. R(y) = 350y c. P(x,y) = 350y − (30000 + 14000x) d. Each car/instructor can serve up to (4 students/session)(2 sessions/course)( courses/year) = 64 students annually. Five cars can serve 320 students. If the classes are filled, then profit for five cars is 350(320) − (30000 + 14000(5)) = 12000. So, the school can reach the break-even point.
POINTS: 1
TOPICS: Break-even analysis
- 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. ANSWER : 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. b. How long it takes to process each job on each machine, and any job-macpairings that are unacceptable. hine
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. d.
Stochastic: job processing times vary due to varying machine set-up times, variable operator performance, and more. e. Assume that processing times are deterministic (known/fixed).
POINTS: 1
TOPICS: Model development
- 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? constraints? the objective function? the
d. Is the model deterministic or stochastic? e. Suggest assumptions that could be made to simplify the model. ANSWER : a. A quantitative approach to decision making can provide a systematic way to
determine a minimum shipping cost from the warehouses to the stores. b. Fixed costs and variable shipping costs; the demand each week at eacsupplies each week at each warehouse. h store; the
c.
Decision variables--how much to ship from each warehouse to each store; objective function--minimize total shipping costs; constraints--meet the demand at the stores without exceeding the supplies at the warehouses.
d.
Stochastic--weekly demands fluctuate as do weekly supplies; transportation costs could vary 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
- 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. B 90,000 4. C 80,000 4.
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 per unit? c. What is the break-even volume for each process?
ANSWER: a. C(x) = FC + VC(x) Process A: C(x) = $120,000 + $3(8,000) = $144,000 per year Process B: C(x) = $ 90,000 + $4(8,000) = $122,000 per year Process C: C(x) = $ 80,000 + $4(8,000) = $116,000 per year Process C has the lowest annual cost for a production volume of 8,000 units.
b. Q = (profit + FC)/(price - VC) Process A: Q = ($50,000 + $120,000)/($6 - $3) = 43,038 units Process B: Q = ($50,000 + $ 90,000)/($6 - $4) = 47,458 units Process C: Q = ($50,000 + $ 80,000)/($6 - $4) = 53,062 units Process A requires the lowest production volume for an annual profit of $50,000.
c. At breakeven, profit (the pretax profits per period) is equal to zero. Q = FC/(price - VC) Process A: Q = $120,000/ ($6 - $3) = 30,380 units Process B: Q = $ 90,000/ ($6 - $4) = 30,509 units Process C: Q = $ 80,000/ ($6 - $4) = 32,654 units Process A has the lowest break-even quantity, while Process B’s is almost as low.
POINTS: 1
TOPICS: Break-even analysis
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?
ANSWER: a. $200X = $190,000 + (.75)($200)X --> ($50)X = $190,000 --> X = 3, b. $250X = $190,000 + (.70)($250)X --> ($75)X = $190,000 --> X = 2, 533
POINTS: 1
TOPICS: Cost and volume models
Essay
- Should the problem solving process be applied to all problems? ANSWER: Answer not provided.
POINTS: 1
TOPICS: Problem solving and decision making
- 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
- 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
- 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
- What steps of the problem solving process are involved in decision making? ANSWER: Answer not provided.
POINTS: 1
TOPICS: Introduction
- Give three benefits of model development and an example of each. ANSWER: Answer not provided.
POINTS: 1
TOPICS: Model development
- 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
- Define and contrast the terms feasible solution, infeasible solution and optimal solution. ANSWER: Answer not provided.
POINTS: 1
TOPICS: Model solution
- Define three forms of models and provide an example of each.
ANSWER: Answer not provided.
POINTS: 1
TOPICS: Model development
- Explain the difference between controllable and uncontrollable inputs to a mathematical model and provide an example of each. ANSWER: Answer not provided.
POINTS: 1
TOPICS: Model development
Chapter 1 Introduction
Course: Linear Programming (236A)
University: University of California Los Angeles
