Resource-time and People Management

Introduction True / False 1. The process of decision making is more limited than that of problem solving. a. True b. Fals e ANSWER: True 2. The terms 'stochastic' and 'deterministic' have the same meaning in quantitative analysis. a. True b. Fals e ANSWER: False 3. The volume that results in marginal revenue equaling marginal cost is called the break-even point. a. True b. Fals e ANSWER: False 4. Problem solving encompasses both the identification of a problem and the action to resolve it. a. True b. Fals e ANSWER: True 5. The decision making process includes implementation and evaluation of the decision. a. True b. Fals e ANSWER: 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. Fals e ANSWER: False 7. 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 8. Uncontrollable inputs are the decision variables for a model. a. True b. Fals e ANSWER: False 9. The feasible solution is the best solution possible for a mathematical model. a. True b. Fals e ANSWER: False 10. 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 11. Frederick Taylor is credited with forming the first MS/OR interdisciplinary teams in the 1940's. a. True b. Fals e ANSWER: False 12. To find the choice that provides the highest profit and the fewest employees, apply a single-criterion decision process. a. True b. Fals e ANSWER: 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. Fals e ANSWER: True 14. The first step in the decision making process is to identify the problem. a. True b. Fals e ANSWER: True 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. Fals e ANSWER: True 16. In quantitative analysis, the optimal solution is the mathematically-best solution. a. True b. Fals e ANSWER: True 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. Fals e ANSWER: True 18. 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 19. A feasible solution is one that satisfies at least one of the constraints in the problem. a. True b. Fals e ANSWER: False 20. A toy train layout designed to represent an actual railyard is an example of an analog model. a. True b. Fals e ANSWER: False 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. ANSWER: d 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. ANSWER: b 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. ANSWER: a 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. ANSWER: c 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. ANSWER: b 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. ANSWER: c 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. ANSWER: a 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. ANSWER: b 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. ANSWER: c 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. ANSWER: a 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. ANSWER: b 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. ANSWER: c 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. ANSWER: c 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. ANSWER: d 35. A model that uses a system of symbols to represent a problem is called a. mathematical . b. iconic. c. analog. d. constrained. ANSWER: a 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 ANSWER: d 37. 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 38. 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 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 ANSWER: b 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 ANSWER: d 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. The manufacturer needs at least 12000 units of corn. The Iowa cooperative can supply up to c. 8000 units, and the Illinois cooperative can supply at least 6000 units. Develop constraints for these conditions. ANSWER a. Let x1 = the number of units from Iowa : Let x2 = the number of units from Illinois b. Min 6x1 + 5.5x2 c. x1 + x 2 ≥ 12000 x1 ≥ 8000 x1 ≥ 6000 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. b. How many units can be sold at the $10 price? How many can be sold at the $50 price? Model the expression for total revenue. Consider prices of $20, $30, and $40. Which of these three price alternative will maximize c. total revenue? What are the values for demand and revenue at this price? ANSWER a. For p = 10, d = 4750 : For p = 50, d = 3750 b. TR = p(5000 −25p) 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) 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. b. c. d. Write an expression for total cost. Write an expression for total revenue. Write an expression for total profit. Find the break-even point. ANSWER a. C(x) = 50000 + 25x : b. R(x) = 45x c. P(x) = 45x −(50000 + 25x) d. x = 2500 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. ANSWER: Let x1 = the number of books sold in the U.S. Let x2 = the number of books sold outside the U.S. 10000 = 1x1 + 1.35x2 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? ANSWER: Enrollment would need to be 10 students. 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) Variable cost per occupied room per night Revenue per occupied room per night $6000 $ 20 $ 75 a. b. c. Write the expression for total cost per month. Assume 30 days per month. Write the expression for total revenue per month. 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) Break-even occupancy = 3.64 or 4 occupied rooms per night, so they have enough c. rooms to break even. This would be a 33% occupancy rate. 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. b. How many students would have to attend for the company to break even? 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 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. b. c. d. cell E12, break-even volume. cell E16, total revenue. cell E17, total cost. cell E19, profit (loss). A B C 1 2 3 4 Break-even calculation 5 6 Selling price per unit 7 8 Costs 9 Fix cost Variable cost per unit 10 11 12 Break-even volume 13 14 Sample calculation 15 Volume Total revenue 16 17 Total cost 18 19 Profit (loss) ANSWER a. =E9/(E6-E10) : b. =E15*E6 c. =E9+E10*E15 d. =E16-E17 D E 10 8400 4.5 2000 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. b. Write a mathematical model representing the store's constraints. 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: Chapter 1 - Introduction 1. Maximize the total pieces of furniture displayed. 2. Maximize the total expected number of daily sales. 3. Maximize the total expected daily profit. ANSWER a. 50s + 30c ≤ 800 : s≥5 c≥5 b. (1) Max s + c (2) Max .03s + .05c (3) Max 6s + 5c 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. ANSWER 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 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? ANSWER: 400 swing sets POINTS: 1 TOPICS: Break-even analysis 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? ANSWER: 80 computers 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. c. d. Write an expression for total revenue. Write an expression for total profit. 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)(8 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. 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. a. b. How could a quantitative approach to decision making be used to solve this problem? What would be the uncontrollable inputs for which data must be collected? Define the decision variables, objective function, and constraints to appear in the c. mathematical model. d. Is the model deterministic or stochastic? e. Suggest some simplifying assumptions for this problem. ANSWER A quantitative approach to decision making can provide a systematic way for : a. 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 b. pairings that are unacceptable. Decision variables: one for each job-machine pairing, taking on a value of 1 if the c. 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. Stochastic: job processing times vary due to varying machine set-up times, d. variable operator performance, and more. e. Assume that processing times are deterministic (known/fixed). 55. Consider a department store that must make weekly shipments of a certain product from two different warehouses to four different stores. a. b. How could a quantitative approach to decision making be used to solve this problem? What would be the uncontrollable inputs for which data must be gathered? What would be the decision variables of the mathematical model? the objective function? the c. constraints? d. Is the model deterministic or stochastic? e. Suggest assumptions that could be made to simplify the model. ANSWER A quantitative approach to decision making can provide a systematic way to : a. determine a minimum shipping cost from the warehouses to the stores. b. c. d. e. Fixed costs and variable shipping costs; the demand each week at each store; the supplies each week at each warehouse. 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. Stochastic--weekly demands fluctuate as do weekly supplies; transportation costs could vary depending upon the amount shipped, other goods sent with a shipment, etc. 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. 56. Three production processes - A, B, and C - have the following cost structure: Process A B C Fixed Cost per Year $120,000 90,000 80,000 Variable Cost per Unit $3.00 4.00 4.50 a. What is the most economical process for a volume of 8,000 units? How many units per year must be sold with each process to have annual profits of $50,000 if b. the selling price is $6.95 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 + $3.00(8,000) = $144,000 per year Process B: C(x) = $ 90,000 + $4.00(8,000) = $122,000 per year Process C: C(x) = $ 80,000 + $4.50(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)/($6.95 - $3.00) = 43,038 units Process B: Q = ($50,000 + $ 90,000)/($6.95 - $4.00) = 47,458 units Process C: Q = ($50,000 + $ 80,000)/($6.95 - $4.50) = 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/ ($6.95 - $3.00) = 30,380 units Process B: Q = $ 90,000/ ($6.95 - $4.00) = 30,509 units Process C: Q = $ 80,000/ ($6.95 - $4.50) = 32,654 units Process A has the lowest break-even quantity, while Process B’s is almost as low. 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 autoassembled 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: Annual fixed cost Variable cost per product Estimated annual production (in number of products): Year 1 Year 2 Year 3 AutoAssembly Process Manual Assembly Process $690,000 $29.56 $269,000 $31.69 152,000 190,000 225,000 152,000 190,000 225,000 a. Which production process would be the least-cost alternative in Years 1, 2, and 3? 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? b. ANSWER: a. C(x) = fixed cost + variable cost(x) Year 1: CA = 690,000 + 29.56(152,000) = $5,183,120 CM = 269,000 + 31.69(152,000) = $5,085,880 (least-cost alternative) Year 2: CA = 690,000 + 29.56(190,000) = $6,306,400 CM = 269,000 + 31.69(190,000) = $6,290,100 (least-cost alternative) Year 3: CA = 690,000 + 29.56(225,000) = $7,341,000 (least-cost alternative) CM = 269,000 + 31.69(225,000) = $7,399,250 b. CA = CM FCA + vA(190,000) = FCM + vM(190,000) 690,000 + v(190,000) = 269,000 + 31.69(190,000) vA = (269,000 + 6,021,100 - 690,000)/190,000 vA = $29.47 (roughly a 0.3% reduction) 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? ANSWER: a. $200X = $190,000 + (.75)($200)X --> ($50)X = $190,000 --> X = 3,800 b. $250X = $190,000 + (.70)($250)X --> ($75)X = $190,000 --> X = 2, 533 Essay 59. Should the problem solving process be applied to all problems? ANSWER: Answer not provided. 60. Explain the difference between quantitative and qualitative analysis from the manager's point of view. ANSWER: Answer not provided. 61. Explain the relationship among model development, model accuracy, and the ability to obtain a solution from a model. ANSWER: Answer not provided. 62. 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. 63. What steps of the problem solving process are involved in decision making? ANSWER: Answer not provided. 64. Give three benefits of model development and an example of each. ANSWER: Answer not provided. 65. Explain the relationship between information systems specialists and quantitative analysts in the solution of large mathematical problems. ANSWER: Answer not provided. 66. Define and contrast the terms feasible solution, infeasible solution and optimal solution. ANSWER: Answer not provided. 67. Define three forms of models and provide an example of each. ANSWER: Answer not provided. 68. Explain the difference between controllable and uncontrollable inputs to a mathematical model and provide an example of each. ANSWER: Answer not provided.