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Business Analytics 2nd Global Edition James R. Evans - Solutions
Find the probability of getting the each of the total values when two dice is rolled: 1, 2, 5, 6, 7, 10, and 11.
The students of a class have elected five candidates to represent them on the college management council:S.No. Gender Age 1 Male 18 2 Male 19 3 Female 22 4 Female 20 5 Male 23 This group decides to elect a spokesperson by randomly drawing a name from a hat. Calculate the probability of the
Refer to the card scenario described in Problem 2.a. Let A be the event “total card value is odd.” Find P(A) and P(Ac).b. What is the probability that the sum of the two cards will be more than 14?
The latest nationwide political poll in a particular country indicates that the probability for the candidate to be a republican is 0.55, a communist is 0.30, and a supporter of the patriots of that country is 0.15. Assuming that these probabilities are accurate, within a randomly chosen group of
From a bag full of colored balls (red, blue, green and orange), some are picked out and replaced. This is done a thousand times and the number of times each colored ball is picked out is—Blue: 300, Red: 200, Green: 450, and Orange: 50.a. What is the probability of picking a green ball?b. What is
A box contains marbles of three different colors:8 black, 6 white, and 4 red. Three marbles are selected at random without replacement. Find the probability that the selection contains each of the outcomes listed.a. Three black marblesb. A red, a black and a white marble, in that orderc. A red
Row 26 of the Excel file Census Education Data gives the number of employed persons having a specific educational level.a. Find the probability that an employed person has attained each of the educational levels listed in the data.b. Suppose that A is the event “has at least an Associate’s
A Canadian business school summarized the gender and residency of its incoming class as follows:Residency Gender Canada United States Europe Asia Other Male 123 24 17 52 8 Female 86 8 10 73 4a. Construct the joint probability table.b. Calculate the marginal probabilities.c. What is the probability
In an example in Chapter 3, we developed the following cross-tabulation of sales transaction data:Region Book DVD Total East 56 42 98 North 43 42 85 South 62 37 99 West 100 90 190 Total 261 211 472a. Find the marginal probabilities that a sale originated in each of the four regions and the marginal
A political candidate running for local office is considering the votes she can get in an upcoming election.Assume that the votes can take on only four possible values. If the candidate assessment is per the given Excel sheet Votes, construct the probability distribution graph.Number of Votes
In the roulette example described in Problem 7, what is the probability that the outcome will be green twice in a row? What is the probability that the outcome will be black twice in a row?
A particular training program has been designed to upgrade the administrative skills of managers. The program is self-administered; the manager requires putting in different number of hours to complete the program. The previous participant’s input indicates that the mean length of time spent on
The weekly demand of a slow-moving product has the following probability mass function:Demand, x Probability, f(x)0 0.2 1 0.4 2 0.3 3 0.1 4 or more 0 Find the expected value, variance, and standard deviation of weekly demand.
The Excel sheet Baseball contains information about a team which is using an automatic pitching machine.If the machine is correctly setup and properly adjusted, it will strike 85 percent of the time. If it is incorrectly set up, it will strike only 35 percent of the time. Past data indicates that
Ravi sells three life insurance policies on an average per week. Use Poisson’s distribution to calculate the probability that in a given week he will sella. some policies.b. two or more policies but less than 5 policies.c. one policy, assuming that there are 5 working days per week.
The number and frequency of Atlantic hurricanes annually from 1940 through 2012 is shown here.Number Frequency 0 5 1 16 2 19 3 14 4 3 5 5 6 4 7 3 8 2 10 1 12 1a. Find the probabilities of 0–12 hurricanes each season using these data.b. Assuming a Poisson distribution and using the mean number of
Verify that the function corresponding to the following figure is a valid probability density function.Then find the following probabilities:a. P1x 6 82b. P1x 7 72c. P16 6 x 6 102d. P18 6 x 6 112 f(x) 0.3 0.1 L 6 8. 12
In determining automobile-mileage ratings, it was found that the mpg (X) for a certain model is normally distributed, with a mean of 33 mpg and a standard deviation of 1.7 mpg. Find the following:a. P1X 6 302b. P128 6 X 6 322c. P1X 7 352d. P1X 7 312e. The mileage rating that the upper 5% of cars
Dev scored 940 on a national mathematics test. The mean test score was 850 with a standard deviation of 100.What proportion of students had a higher score than Dev? (Assume that the test scores are normally distributed.)
Develop a procedure to sample from the probability distribution of soft-drink choices in Problem 1.Implement your procedure on a spreadsheet and use the VLOOKUP function to sample 10 outcomes from the distribution.
Develop a procedure to sample from the probability distribution of two-card hands in Problem 2.Implement your procedure on a spreadsheet and use the VLOOKUP function to sample 20 outcomes from the distribution.
Use formula (5.23) to obtain a sample of 25 outcomes for a game of Battleship™ as described in Problem 34.Find the average and standard deviation for these 25 outcomes.
Use the Excel Random Number Generation tool to generate 100 samples of the number of customers that the financial consultant in Problem 31 will have on a daily basis. What percentage will meet his target of at least 5?
Use Analytic Solver Platform to fit the hurricane data in Problem 32 to a discrete distribution? Does the Poisson distribution give the best fit?
For the mower test data, what distribution might be appropriate to model the failure of an individual mower?PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test performance of its mowers after
What fraction of mowers fails the functional performance test using all the mower test data?PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test performance of its mowers after assembly;
What is the probability of having x failures in the next 100 mowers tested, for x from 0 to 20?PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test performance of its mowers after assembly;
What is the average blade weight and how much variability is occurring in the measurements of blade weights?PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test performance of its mowers after
Assuming that the data are normal, what is the probability that blade weights from this process will exceed 5.20?PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test performance of its mowers
What is the probability that weights will be less than 4.80?PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test performance of its mowers after assembly; results from the past 30 days are
What is the actual percent of weights that exceed 5.20 or are less than 4.80 from the data in the worksheet?PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test performance of its mowers after
Is the process that makes the blades stable over time?That is, are there any apparent changes in the pattern of the blade weights?PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test
Could any of the blade weights be considered outliers, which might indicate a problem with the manufacturing process or materials?PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test
Was the assumption that blade weights are normally distributed justified? What is the best-fitting probability distribution for the data?PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test
State the characteristics of some generic types of linear optimization models.
Describe the different categories of constraints that are typically used in optimization models.
Build linear optimization models for a variety of applications.
Use Excel to evaluate scenarios and visualize results for linear optimization models and gain practical insights into the solutions.
Correctly interpret the Solver Sensitivity report for models that have bounded variables.
Use auxiliary variables to model bound constraints and obtain more complete sensitivity information.
Ensure that assumptions underlying the use of sensitivity information hold when interpreting Solver reports.
An airlines corporation is considering the purchase of jet passenger planes so as to increase their passenger service. The type A plane costs $450 million each, the type B costs $400 million each, and the type C costs $250 million each. The corporation has budgeted $50 billion for the purchase of
The Martinez Model Car Company produces four different radio-controlled model cars based on exotic production models: Ferrari, BMW, Lotus, and Tesla.Each model requires production in five departments:molding, sanding, polishing, painting, and finishing.The number of minutes required for each
An international toy manufacturing company manufactures three types of stuffed animals – dog, lion and giraffe, each made from different combination of red, yellow and blue cloth and cotton. The data (cloth requirement in yards) is as below:Toy Dog Lion Giraffe Red 1/2 1/2 1.5 Yellow 2 1.5 1.5
Young Energy operates a power plant that includes a coal-fired boiler to produce steam to drive a generator.The company can purchase different types of coals and blend them to meet the requirements for burning in the boiler. The following table shows the characteristics of the different types of
Holcomb Candles, Inc., manufactures decorative candles and has contracted with a national retailer to supply a set of special holiday candles to its 8,500 stores. These include large jars, small jars, large pillars, small pillars, and a package of four votive candles.In negotiating the contract for
The Children’s Theater Company is a nonprofit corporation managed by Shannon Board. The theater performs in two venues: Kristin Marie Hall and the Lauren Elizabeth Theater. For the upcoming season, seven shows have been chosen. The question Shannon faces is how many performances of each of the
Jaycee’s department store chain is planning to open a new store. It needs to decide how to allocate the 100,000 square feet of available floor space among seven departments. Data on expected performance of each department per month, in terms of square feet(sf), are shown next.Risk as a % of $
A recent MBA graduate, Dara, has gained control over custodial accounts that her parents had established.Currently, her money is invested in four funds, but she has identified several other funds as options for investment. She has $100,000 to invest with the following restrictions:• Keep at least
Janette Douglas is coordinating a bake sale for a nonprofit organization. The organization has acquired$2,200 in donations to hold the sale. The following table shows the amounts and costs of ingredients used per batch of each baked good.Peanut Butter Cups Shortbread Cookies Cost/Unit Butter (cups)
Kelly Foods has two plants and ships canned vegetables to customers in four cities. The cost of shipping one case from a plant to a customer is given in the following table.Plant/Customer Chicago Cincinnati Indianapolis Pittsburgh Akron $1.70 $2.30 $2.50 $2.15 Evansville $1.95 $2.35 $1.65 $2.95 The
Liquid Gold, Inc., transports radioactive waste from nuclear power plants to disposal sites around the country. Each plant has an amount of material that must be moved each period. Each site has a limited capacity per period. The cost of transporting between sites is given in the accompanying table
Shafer Office Supplies has four distribution centers, located in Atlanta, Lexington, Milwaukee, and Salt Lake City, and ships to 12 retail stores, located in Seattle, San Francisco, Las Vegas, Tuscon, Denver, Charlotte, Minneapolis, Fayetteville, Birmingham, Orlando, Cleveland, and Philadelphia.
Roberto’s Honey Farm in Chile makes five types of honey: cream, filtered, pasteurized, mélange (a mixture of several types), and strained, which are sold in 1-kilogram or 0.5-kilogram glass containers, 1-kilogram and 0.75-kilogram plastic containers, or in bulk. Key data are shown in the
Sandford Tile Company makes ceramic and porcelain tile for residential and commercial use. They produce three different grades of tile (for walls, residential flooring, and commercial flooring), each of which requires different amounts of materials and production time, and generates different
The Hansel Corporation, located in Bangalore, India, makes plastics materials that are mixed with various additives and reinforcing materials before being melted, extruded, and cut into small pellets for sale to other manufacturers. Four grades of plastic are made, each of which might include up to
Mirza Manufacturing makes four electronic products, each of which comprises three main materials:magnet, wiring, and casing. The products are shipped to three distribution centers in North America, Europe, and Asia. Marketing has specified that no location should receive more than the maximum
A furniture manufacturing company planes to make three products – chairs, tables and desks from its available weekly resources, which consist of 400 cubic feet of timber and 500 man-hours of labor. To make a chair, it requires 5 cubic feet of timber and 10 manhours of labor and yields a profit of
Reddy & Rao (R&R) is a small company in India that makes handmade artistic chairs for commercial businesses. The company makes four models. The time required to make each of the models and cost per chair is given below.Model A Model B Model C Model D Cost per Unit $900.00 $650.00 $500.00 $750.00
Jason Wright is a part-time business student who would like to optimize his financial decisions. Currently, he has $16,000 in his savings account. Based on an analysis of his take-home pay, expected bonuses, and anticipated tax refund, he has estimated his income for each month over the next year.
Pavlick Products supplies a key component for automobile interiors to U.S. assembly plants. The components can be manufactured in China or Mexico.Unit cost in China is $333, and the unit cost in Mexico is $350. However, shipping costs per 500 units are $10,000 from China, and only $2,000 from
Michelle is a business student who plans to attend medical school. The average state university medical school education expense can cost around $35,000 per year and is escalating rapidly. Michelle created a spreadsheet model to calculate the total expenses for each year of medical school,
Marketing managers have various media alternatives, such as radio, TV, magazines, and so on, in which to advertise and must determine which to use, the number of insertions in each, and the timing of insertions to maximize advertising effectiveness within a limited budget. Suppose that three media
Klein Industries manufactures three types of portable air compressors: small, medium, and large, which have unit profits of $20.50, $34.00, and $42.00, respectively. The projected monthly sales are as follows:Small Medium Large Minimum 14,000 6,200 2,600 Maximum 21,000 12,500 4,200 The production
Fruity Juices, Inc., produces five different flavors of fruit juice: apple, cherry, pomegranate, orange, and pineapple. Each batch of product requires processing in three departments (blending, straining, and bottling).The relevant data (per 1,000-gallon batches)are shown next.Time Required in
Worley Fluid Supplies produces three types of fluidhandling equipment: control valves, metering pumps, and hydraulic cylinders. All three products require assembly and testing before they can be shipped to customers.Control Valve Metering Pump Hydraulic Cylinder Assembly time (min) 45 20 30 Testing
Recognize when to use integer variables in optimization models.
Incorporate integer variables into Solver models.
Develop integer optimization models for practical applications such as workforce scheduling and location.
Find alternative optimal solutions to integer optimization models.
Formulate and solve optimization models with binary variables and logical constraints.
Develop and solve mixed-integer optimization models such as facility location and fixed-cost models.
Evaluate risk in solutions to optimization models using Monte Carlo simulation.
Solve optimization models with chance constraints.
Use multiple parameterized simulations in Analytic Solver Platform to find optimal solutions in simulation models with decision variables.
Use Analytic Solver Platform to combine simulation modeling and optimization to maximize or minimize the expected value of a model output.
Incorporate uncertainty into optimization models such as project selection.
Recognize when to use nonlinear optimization models.
Develop and solve nonlinear optimization models for different applications.
Interpret Solver reports for nonlinear optimization.
Use empirical data and line-fitting techniques in nonlinear optimization.
Recognize a quadratic optimization model.
Identify non-smooth optimization models and when to use Evolutionary Solver.
Formulate and solve sequencing and scheduling models using Solver’s all different constraint.
Solve Problem 6 in Chapter 13 to ensure that the number of minutes of each type of ad are integer valued. How much difference is there between the optimal integer solution and the linear optimization solution? Would rounding the continuous solution have provided the optimal integer solution?
Solve the Toy Manufacturing model in Problem 5 of Chapter 14 with the restriction that the number of units manufactured must be an integer. Compare your solution with the linear optimization solution.
Solve the media selection model in Problem 21 of Chapter 14 with the restriction that the number of ads placed must be integer. Compare your solution with the linear optimization solution.
Solve the following as integer optimization model:Maximize Z = a + 4b; subject to 2a + 4b 6= 7; 5a +3b 6= 15; anda, b are integers satisfying non-negativity constraints.
The Gardner Theater, a community playhouse, needs to determine the lowest-cost production budget for an upcoming show. Specifically, they have to determine which set pieces to construct and which, if any, set pieces to rent from another local theater at a predetermined fee. However, the
Van Nostrand Hospital must schedule nurses so that the hospital’s patients are provided with adequate care. At the same time, in the face of tighter competition in the health-care industry, careful attention must be paid to keeping costs down. From historical records, administrators can project
Joe is an active 26-year-old male who lifts weights 6 days a week. His rigorous training program requires a diet that will help his body recover efficiently. He is also a graduate student who is looking to minimize the cost of consuming his favorite foods. Joe is trying to gain weight, or at least
Jubilee Works has three types of jobs in one of its plant and needs to assign it to three men. Each assignment of a man to a job fetches different cost of performing that job. The data below shows the cost matrix ($) for assignment of the three men to three jobs.J1 J2 J3 M1 5 8 9 M2 6 7 11 M3 8 9
A building contractor has just won a contract to build a municipal library building. His present labor work force is inadequate to take this work immediately as he has already got other jobs on hand.Therefore he can either hire new labor on full-time basis (for 8-hours day each) at $80 per day or
Fuller Legal Services wants to determine how much time to allocate to four different services: business consulting, criminal work, nonprofit consulting, and wills/trusts. Mr. Fuller has determined the average hourly fees and the minimum and maximum hours(for consulting and criminal work) and cases
Four items are considered for loading on an airplane, which has a capacity to load up to 25 metric ton. The weights and values of the items are provided in the table. Which items and what quantities should be loaded onto the plane so as to maximize the value of the cargo transported?Formulate this
A software-support division of Blain Information Services has eight projects that can be performed.Each project requires different amounts of development time and testing time. In the coming planning period, 1,150 hours of development time and 900 hours of testing time are available, based on the
The Kelmer Performing Arts Center offers a series of four programs that includes jazz, bluegrass, folk, classical, and comedy. The Program Coordinator needs to determine which acts to choose for next year’s series. She assigned an “impact” rating to each artist that reflects how well the act
Dannenfelser Design works with clients in three major project categories: architecture, interior design, and combined. Each type of project requires an estimated number of hours for different categories of employees, as shown in the following table.Architecture Interior Design Combined Hourly Rate
Anya is a part-time business student who works full time and is constantly on the run. She recognized the challenge of eating a balanced diet and wants to minimize cost while meeting some basic nutritional requirements. Based on some research, she found that a very active woman should consume 2,250
Josh Steele manages a professional choir in a major city. His marketing plan is focused on generating additional local demand for concerts and increasing ticket revenue and also gaining attention at the national level to build awareness of the ensemble across the country. He has $20,000 to spend on
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