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quantitative analysis for management
Quantitative Analysis For Management 12th Edition Barry Render, Ralph M. Stair, Michael E. Hanna - Solutions
=15-2 Why are x- and R-charts usually used hand in hand?
=15-1 Why is the central limit theorem so important in quality control?
=10. If a process only has random variations (it is in control), then 95.5% of the time the sample averages will fall withina. 1 standard deviation of the population mean.b. 2 standard deviations of the population mean.c. 3 standard deviations of the population mean.d. 4 standard deviations of the
=9. A machine is supposed to fill soft drink cans to 12 ounces. It appears that although the average amount in the cans is about 12 ounces (based on sample means), there is a great deal of variability in each of the individual cans. The type of chart that would best detect this problem would bea. a
=8. After a control chart (for means) has been developed, samples are taken and the average is computed for each sample. The process could be considered out of control ifa. one of the sample means is above the upper control limit.b. one of the sample means is below the lower control limit.c. five
=7. A company is implementing a new quality control program. Items are sampled and classified as being defective or nondefective. The type of control chart that should be used isa. an R-chart.b. a control chart for variables.c. a control chart for attributes.d. a control limit chart.
=6. A type of variability that indicates that a process is out of control is calleda. natural variation.b. assignable variation.c. random variation.d. average variation.
=5. The Poisson distribution is often used witha. R-charts.b. p-charts.c. c-charts.d. x-charts.
=4. Control charts for attributes area. p-charts.b. m-charts.c. R-charts.d. x-charts.
=3. The type of chart used to control the number of defects per unit of output is thea. x-chart.b. R-chart.c. p-chart.d. c-chart.
=2. A control chart for monitoring processes in which values are measured in continuous units such as weight or volume is called a control chart fora. attributes.b. measurements.c. variables.d. quality.
=1. The degree to which the product or service meets specifications is one definition ofa. sigma.b. quality.c. range.d. process variability.
=2. In a mixed-integer programming problema. some integers must be even and others must be odd.b. some decision variables must require integer results only and some variables must allow for continuous results.c. different objectives are mixed together even though they sometimes have relative
=4. An integer programming solution can never produce a greater profit than the LP solution to the same problem.a. Trueb. False
=5. In goal programming, if all the goals are achieved, the value of the objective function will always be zero.a. Trueb. False
=6. The objective in a goal programming problem with one priority level is to maximize the sum of the deviational variables.a. Trueb. False
=7. Nobel Laureate Herbert A. Simon of Carnegie-Mellon University says that modern managers should always optimize, not satisfice.a. Trueb. False
=9. The 0–1 integer programming problema. requires the decision variables to have values between 0 and 1.b. requires that the constraints all have coefficients between 0 and 1.c. requires that the decision variables have coefficients between 0 and 1.d. requires the decision variables to be equal
=10-1 Compare the similarities and differences of linear and goal programming.
=10-3 List the advantages and disadvantages of solving integer programming problems by (a) rounding off and (b) enumeration.
=10-4 What is the difference between the three types of integer programming problems? Which do you think is most common, and why?
=10-5 What is meant by “satisficing,” and why is the term often used in conjunction with goal programming?
=10-6 What are deviational variables? How do they differ from decision variables in traditional LP problems?
=10-8 What does it mean to rank goals in goal programming? How does this affect the problem’s solution?
=10-9 Which of the following are NLP problems, and why?(a) Maximize profit subject to= + +≥≤≥3 5 99 10 518 1 2 3 12 3X X X XX X(b) Maximize cost subject to= + +≥+ ≥25 30 8 812 0 0005 1 2 1 2 11 2 X X X X XX X. X1 2 − = X 11(c) Maximize subject to 1 Z Pd P d P X X d d X d= + ++ + −
=10-11 A group of college students is planning a camping trip during the upcoming break. The group must hike several miles through the woods to get to the campsite, and anything that is needed on this trip must be packed in a knapsack and carried to the campsite. One particular student, Tina Shawl,
= 10-14 Trapeze Investments is a venture capital firm that is currently evaluating six different investment opportunities. There is not sufficient capital to invest in all of these, but more than one will be selected. A 0–1 integer programming model is planned to help determine which of the six
=(c) If investment 4 is selected, then investment 6 must also be selected. However, if investment 4 is not selected, it is still possible to select number 6.(d) Investment 5 cannot be selected unless both investments 2 and 3 are also selected.(e) Investment 5 must be selected if both investments 2
=10-15 Horizon Wireless, a cellular telephone company, is expanding into a new era. Relay towers are necessary to provide wireless telephone coverage to the different areas of the city. A grid is superimposed on a map of the city to help determine where the towers should be located. The grid
=10-16 Innis Construction Company specializes in building moderately priced homes in Cincinnati, Ohio.Tom Innis has identified eight potential locations to construct new single-family dwellings, but he cannot put up homes on all of the sites because he has only $300,000 to invest in all projects.
=10-17 A real estate developer is considering three possible projects: a small apartment complex, a small shopping center, and a mini-warehouse. Each of these requires different funding over the next two years, and the net present value of the investments also varies. The following table provides
=10-19 Triangle Utilities provides electricity for three cities. The company has four electric generators that are used to provide electricity. The main generator operates 24 hours per day, with an occasional shutdown for routine maintenance. Three other generators (1, 2, and 3) are available to
=3. These generators are used in the following ways:A generator may be started at 6:00 a.m. and run for either 8 hours or 16 hours, or it may be started at 2:00 p.m. and run for 8 hours (until 10:00 p.m.). All generators except the main generator are shut down at 10:00 p.m. Forecasts indicate the
=(a) Formulate this problem as an integer programming problem to determine the least-cost way to meet the needs of the area.
=(b) Solve using computer software.
=10-20 The campaign manager for a politician who is running for reelection to a political office is planning the campaign. Four ways to advertise have been selected: TV ads, radio ads, billboards, and newspaper ads. The cost of these are $900 for each TV ad,$500 for each radio ad, $600 for a
=1. The number of people reached should be at least 1,500,000.
=2. The total monthly advertising budget should not be exceeded.
=3. Together, the number of ads on either TV or radio should be at least 6.
=4. No more than 10 ads of any one type of advertising should be used.(a) Formulate this as a goal programming problem.(b) Solve this using computer software.(c) Which goals are exactly met and which of them are not?
=10-21 Geraldine Shawhan is president of Shawhan File Works, a firm that manufactures two types of metal file cabinets. The demand for her two-drawer model is up to 600 cabinets per week; demand for a threedrawer cabinet is limited to 400 per week. Shawhan File Works has a weekly operating
=1. Attain a profit as close to $11,000 as possible each week.
=2. Avoid underutilization of the firm’s production capacity.
=3. Sell as many two- and three-drawer cabinets as the demand indicates.Set this up as a goal programming problem.
=10-22 Solve Problem 10-21. Are any goals unachieved in this solution? Explain.
=10-23 Hilliard Electronics produces specially coded computer chips for laser surgery in 64MB, 256MB, and 512MB sizes. (1MB means that the chip holds 1 million bytes of information.) To produce a 64MB chip requires 8 hours of labor, a 256MB chip takes 13 hours, and a 512MB chip requires 16 hours.
=1. Fill an order from the best customer for thirty 64MB chips and thirty-five 256MB chips.
=2. Provide sufficient chips to at least equal the sales estimates set by Mr. Blank.
=3. Avoid underutilization of the production capacity.Formulate this problem using goal programming.
=10-24 An Oklahoma manufacturer makes two products:speaker telephones (X1) and pushbutton telephones(X2). The following goal programming model has been formulated to find the number of each to produce each day to meet the firm’s goals:Minimize subject to P d P d P d P d X X d d 1 1 2 2 3 3 4 1 1
=10-25 Major Bill Bligh, director of the Army War College’s new 6-month attaché training program, is concerned about how the 20 officers taking the course spend their precious time while in his charge.Major Bligh recognizes that there are 168 hours per week and thinks that his students have
=10-29 During the busiest season of the year, Green-Gro Fertilizer produces two types of fertilizers. The standard type (X) is just fertilizer, and the other type (Y)is a special fertilizer and weed-killer combination.The following model has been developed to determine how much of each type
=10-30 Pat McCormack, a financial advisor for Investors R Us, is evaluating two stocks in a particular industry. He wants to minimize the variance of a portfolio consisting of these two stocks, but he wants to have an expected return of at least 9%. After obtaining historical data on the variance
=10-31 Summertime Tees sells two very popular styles of embroidered shirts in southern Florida: a tank top and a regular T-shirt. The cost of the tank top is$6, and the cost of the T-shirt is $8. The demand for these is sensitive to the price, and historical data indicate that the weekly demands
=10-34 Using the data in Solved Problem 10-3, develop a spreadsheet for a 2-period weighted moving average forecast with weights of 0.6 (w1)for the most recent period and 0.4 (w2) for the other period. Note these weights sum to 1, so the forecast is simply Forest for next period Value in current
=10-35 A line manager plans to complete six jobs on machines that have already been selected. It wishes to accomplish this over the next five time periods.Conceivably, it could complete all the jobs in period 1 or wait to complete all the jobs in period 5. More likely, it will build complete one
=10-36 Assume that one is given the following means, standard deviations, and correlations for the annual return on three stocks.STOCK 1 STOCK 2 STOCK 3 Mean return 0.15 0.18 0.23 S. D of return 0.15 0.14 0.18 CORRELATION MATRIX STOCK 1 STOCK 2 STOCK 3 Stock 1 1 0.52 0.35 Stock 2 0.52 1 0.49 Stock
=1. If Schank were not concerned about noncost goals, how would he formulate this problem so that it could be solved quantitatively?
=2. Develop a formulation that will incorporate all five objectives.
=1. Determine the minimum number of toll collectors that would have to be hired to meet the requirements expressed in the table.
=2. The union had indicated that it might lift its opposition to the mixing of shifts in a 5-day block in exchange for additional compensation and benefits. By how much could the number of toll collectors required be reduced if this is done?
=1. The crude is transported from various ports across the world and then through pipelines from the ports to the refineries. Model the purchase and transportation of crude oil as a mixed integer programming problem.
=2. Solve the problem using any available Integer Programming solver.
=3. Information on rail freight transportation cost is given in Table 10.11. How can we compare the transportation cost through pipeline with the rail freight?
=7. In PERT, slack time equalsa. EF + t.b. LS - ES.c. 0.d. EF - ES.e. none of the above.
=11. If activity A is not on the critical path, then the slack for A will equala. LF - EF.b. EF - ES.c. 0.d. all of the above.
=13. activities are ones that will delay the entire project if they are late or delayed.
=14. PERT stands for .
=15. Project crashing can be performed using a.
=16. PERT can use three estimates for activity time. These three estimates are , , and .
=17. The latest start time minus the earliest start time is called the time for any activity.
=18. The percent of project completion, value of work completed, and actual activity costs are used to ______________ projects.
=11-1 What are some of the questions that can be answered with PERT and CPM?
=11-2 What are the major differences between PERT and CPM?
=11-3 What is an activity? What is an event? What is an immediate predecessor?
=11-4 Describe how expected activity times and variances can be computed in a PERT network.
=11-5 Briefly discuss what is meant by critical path analysis. What are critical path activities, and why are they important?
=11-6 What are the earliest activity start time and latest activity start time? How are they computed?
=11-7 Describe the meaning of slack and discuss how it can be determined.
=11-8 How can we determine the probability that a project will be completed by a certain date? What assumptions are made in this computation?
=11-9 Briefly describe PERT/Cost and how it is used.
=11-10 What is crashing, and how is it done by hand?
=11-11 Why is linear programming useful in CPM crashing?
=11-13 Sid Davidson was able to determine the activity times for the leadership training program. He would like to determine the total project completion time and the critical path. The activity times appear in the following table (see Problem 11-12):Activity Time (Days)A 2 B 5 C 1 D 10 E 3 F 6 G 8
=11-14 Jean Walker is making plans for spring break at the beaches in Florida. In applying techniques she learned in her quantitative methods class, she has identified the activities that are necessary to prepare for her trip. The following table lists the activities and the immediate predecessors.
=11-15 The following are the activity times for the project in Problem 11-14. Find the earliest, latest, and slack times for each activity. Then find the critical path.Activity Time (Days)A 3 B 7 C 4 D 2 E 5 F 6 G 3
=11-17 After consulting with Butch Radner, George Monohan was able to determine the activity times for constructing the weed-harvesting machine to be used on narrow rivers. George would like to determine ES, EF, LS, LF, and slack for each activity. The total project completion time and the critical
=11-18 A project was planned using PERT with three time estimates. The expected completion time of the project was determined to be 40 weeks. The variance of the critical path is 9.(a) What is the probability that the project will be finished in 40 weeks or less?(b) What is the probability that
=(c) What is the probability that the project will be finished in 46 weeks or less?
=(d) What is the probability that the project will take longer than 46 weeks?
=(e) The project manager wishes to set the due date for the completion of the project so that there is a 90% chance of finishing on schedule. Thus, there would only be a 10% chance the project would take longer than this due date. What should this due date be?
=11-19 Tom Schriber, a director of personnel of Management Resources, Inc., is in the process of designing a program that its customers can use in the job-finding process. Some of the activities include preparing resumés, writing letters, making appointments to see prospective employers,
=(d) Determine the critical path and project completion time.
=(e) Determine the probability that the project will be finished in 70 days or less.
=(f) Determine the probability that the project will be finished in 80 days or less.
=(g) Determine the probability that the project will be finished in 90 days or less.
=11-20 Using PERT, Ed Rose was able to determine that the expected project completion time for the construction of a pleasure yacht is 21 months and the project variance is 4.
=(a) What is the probability that the project will be completed in 17 months or less?
=(b) What is the probability that the project will be completed in 20 months or less?
=(c) What is the probability that the project will be completed in 23 months or less?(d) What is the probability that the project will be completed in 25 months or less?
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