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Business Analytics Methods Models And Decisions 1st Edition James R. Evans - Solutions
16. For the Shafer Office Supplies problem (Problem 13 in Chapter 14), suppose that the company wants to enforce a single sourcing constraint that each retail store be served only from one distribution center. Set up and solve a model to find the minimum cost solution.
15. For the General Appliance Corporation transportation model discussed in Chapter 14, suppose that the company wants to enforce a single sourcing constraint that each retail store be served from only one distribution center. Set up and solve a model to find the minimum cost solution.
14. Soapbox is a local band that plays classic and contemporary rock. The band members charge $600 for a 3-hour gig. They would like to play at least 30 gigs per year but need to determine the best way to promote themselves. The most they are willing to spend on promotion is $2,500. The possible
13. 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
12. 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
11. 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 table.Architecture Interior Design Combined Hourly Rate
10. 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
9. Riesemberg Medical Devices is allocating next year’s budget among its divisions.As a result, the R&D Division needs to determine which R&D projects to fund.Each project requires various software and hardware and consulting expenses, along with internal human resources. A budget allocation of
8. The personnel director of Hatch Financial. which recently absorbed another firm, is now downsizing and must relocate five information systems analysts from recently closed locations. Unfortunately, there are only three positions available for five people.Salaries are fairly uniform among this
7. Gales Products manufactures ribbon for thermal transfer printing, which transfers ink from a ribbon onto paper through a combination of heat and pressure. Different types of printers use different sizes of ribbons. The company has forecasted demands for seven different ribbon sizes:Size Forecast
6. 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
5. For the Brewer Services scenario described in this chapter, suppose that 11 permanent employees are hired. Find an optimal solution to minimize the number of part-time employees he needs to hire.
4. Solve the media selection model in Problem 3 of Chapter 21 with the restriction that the number of ads placed must be integer. Compare your solution with the linear optimization solution.
3. Solve the Rosenberg Land Development model in Problem 2 of Chapter 14 with the restriction that the number of units built must be integer. Compare your solution with the linear optimization solution.
2. Solve the J&M Manufacturing model in Chapter 14 to ensure that the number of units produced is integer valued. How much difference is there between the optimal integer solution and the linear optimization solution?
1. Solve the D. A. Branch & Sons model in Chapter 14 to ensure that the investments are integer valued. How much difference is there between the optimal integer solution and the linear optimization solution?
• Develop and solve mixed-integer optimization models such as facility location and fixed-cost models.
• Formulate and solve optimization models with binary variables and logical constraints.
• Find alternative optimal solutions to integer optimization models.
• Develop integer optimization models for practical applications such as workforce scheduling and location.
• Incorporate integer variables into Solver models.
• Recognize when to use integer variables in optimization models.
25. Beverly Ann Cosmetics has created two new perfumes: Summer Passion and Ocean Breeze. It costs $5.25 to purchase the fragrance needed for each bottle of Summer Passion and $4.70 for each bottle of Ocean Breeze. The marketing department has stated that at least 30% but no more than 70% of the
24. Worley Fluid Supplies produces three types of fluid-handling 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
23. 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
22. 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
21. Marketing managers have various media alternatives, such as radio, TV, magazines, etc., 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
20. 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
19. An international graduate student will receive a $28,000 foundation scholarship and reduced tuition. She must pay $1,500 in tuition for each of the autumn, winter, and spring quarters, and $500 in the summer. Payments are due on the first day of September, December, March, and May,
18. Raturi and Rao, Inc., produces four industrial chemicals with variable production costs of $9.00, $6.75, $5.25, and $7.50 per pound, respectively. Because of increasing supplier costs, the variable cost of each of the products will increase by 6% at the beginning of month 3. Demand forecasts
17. 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
16. 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
15. 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
14. 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
13. 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 Pittsburgh.
12. 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 here (some
11. 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
10. 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.Ingredient Brownies Cupcakes Peanut Butter Cups
9. 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
8. 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.Department
7. 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
6. 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
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
4. The International Chef, Inc., markets three blends of oriental tea: premium, Duke Grey, and breakfast. The firm uses tea leaves from India, China, and new domestic California sources.Tea Leaves (Percent)Quality Indian Chinese California Premium 40 20 40 Duke Grey 30 50 20 Breakfast 40 40 20 Net
3. Korey is a business student at State U. She has just completed a course in decision models, which had a midterm exam, a final exam, individual assignments, and class participation. She earned an 86% on the midterm, 94% on the final, 93% on the individual assignments, and 85% on participation.
2. Rosenberg Land Development (RLD) is a developer of condominium properties in the Southwest United States. RLD has recently acquired a 40.625-acre site outside Phoenix, Arizona. Zoning restrictions allow at most 8 units per acre. Three types of condominiums are planned: one-, two-, and
1. Classify the following descriptions of constraints as bounds, limitations, requirements, proportional relationships, or balance constraints:a. Each serving of chili should contain a quarter pound of beef.b. Customer demand for a cereal is not expected to exceed 800 boxes during the next month.c.
• Ensure that assumptions underlying the use of sensitivity information hold when interpreting Solver reports.
• Use auxiliary variables to model bound constraints and obtain more complete sensitivity information.
• Correctly interpret the Solver Sensitivity report for models that have bounded variables.
• Use Excel to evaluate scenarios for linear optimization models and gain practical insights into the solutions.
• Build linear optimization models for a variety of applications.
• Describe the different categories of constraints that are typically used in optimization models.
• State the characteristics of some generic types of linear optimization models.
21. Conduct a Solver parameter analysis for the number of components A available in the Valencia Products model in Problem 1. Define the parameter range from 4,000 to 4,500 in increments of 100.
20. Conduct a Solver parameter analysis for the unit profit of Deercrest skis in the SSC model. Define the parameter range from $65 to $80 in increments of $5.
19. Figure 13.33 shows the Solver sensitivity report for the investment scenario in Problem 4. Using only the information in the sensitivity report, answer the following questions.a. How much would the return on stock B have to increase in order to invest fully in that stock?b. How much would the
18. Figure 13.32 shows the Solver sensitivity report for the Burger Office Equipment scenario in Problem 3. Using only the information in the sensitivity report, answer the following questions.a. Explain the reduced cost associated with standard desks.b. If 25% of the oak is deemed to be
17. Figure 13.31 shows the Solver sensitivity report for the ColPal Products scenario in Problem 2. Using only the information in the sensitivity report, answer the following questions.a. Suppose that the exposure for TV advertising was incorrectly estimated and should have been 875. How would the
16. Figure 13.30 shows the Solver sensitivity report for Valencia Products in Problem 1. Using only the information in the sensitivity report, answer the following questions.a. Explain why the reduced cost for SpeedBuster is 0.b. If the unit profit for LaserStop is decreased to $20, can you predict
15. Figure 13.29 shows the sensitivity report after solving the Crebo Manufacturing model (Example 13.12) using Solver. Using only the information in the sensitivity report, answer the following questions.a. Explain the value of the reduced cost (–0.3) for the number of plugs to produce.b. If the
14. For the investment situation in Problem 4, apply the same logic as we did for the Crebo Manufacturing model in the text to find the optimal solution. Compare your answer with the Solver solution.
13. For ColPal Products in Problem 2, modify the data in the model to create a problem with each of the followinga. alternative optimal solutionsb. an unbounded solutionc. infeasibility
12. For Valencia Products in Problem 1, modify the data in the model to create a problem with each of the following.a. alternative optimal solutionsb. an unbounded solutionc. infeasibility
11. For the Burger Office Equipment model in Problem 3, graph the constraints and identify the feasible region. Then identify each of the corner points and show how increasing the objective function value identifies the optimal solution.
10. For ColPal model in Problem 2, graph the constraints and identify the feasible region. Then identify each of the corner points and show how increasing the objective function value identifies the optimal solution.
9. For the Valencia Products model in Problem 1, graph the constraints and identify the feasible region. Then identify each of the corner points and show how increasing the objective function value identifies the optimal solution.
8. Implement the linear optimization model that you developed for the investment scenario in Problem 4 in Excel and use Solver to find an optimal solution. Save the Answer and Sensitivity reports in your Excel workbook. Interpret the Solver Answer report and identify the binding constraints and
7. Implement the linear optimization model that you developed for Burger Office Equipment in Problem 3 in Excel and use Solver to find an optimal solution. Interpret the Solver Answer report and identify the binding constraints and verify the values of the slack variables by substituting the
6. Implement the linear optimization model that you developed for ColPal Products in Problem 2 in Excel and use Solver to find an optimal solution. Interpret the Solver Answer report and identify the binding constraints and verify the values of the slack variables by substituting the optimal
5. Implement the linear optimization model that you developed for Valencia Products in Problem 1 in Excel and use Solver to find an optimal solution. Interpret the Solver Answer report and identify the binding constraints and verify the values of the slack variables by substituting the optimal
4. A business student has $2,500 available from a summer job and has identified three potential stocks in which to invest. The cost per share and expected return over the next 2 years is given in the table.Stock A B C Price/share $25 $15 $40 Return/share $12 $7 $12a. Identify the decision
3. Burger Office Equipment produces two types of desks, standard and deluxe. Deluxe desks have oak tops and more-expensive hardware and require additional time for finishing and polishing. Standard desks require 80 board feet of pine and 10 hours of labor, whereas deluxe desks require 60 board feet
2. A brand manager for ColPal Products must determine how much time to allocate between radio and television advertising during the next month. Market research has provided estimates of the audience exposure for each minute of advertising in each medium, which it would like to maximize. Costs per
1. Valencia Products makes automobile radar detectors and assembles two models:LaserStop and SpeedBuster. The firm can sell all it produces. Both models use the same electronic components. Two of these can be obtained only from a single supplier. For the next month, the supply of these is limited
• Use the Sensitivity Report to evaluate scenarios.
• Interpret the Solver Sensitivity Report.
• Use Solver for conducting what-if analysis of optimization models.
• List the four possible outcomes when solving a linear optimization model and recognize them from Solver messages.
• Explain how Solver works.
• Illustrate and solve two-variable linear optimization problems graphically.
• Interpret the Solver Answer Report.
• Use the standard and premium Solver add-ins to solve linear optimization models in Excel.
• Implement linear optimization models on spreadsheets.
• State the properties that characterize linear optimization models.
• Recognize different types of constraints in problem statements.
• Apply the four-step process to develop a mathematical model for an optimization problem.
16. The Excel file Myatt Steak House provides 5 years of data on key business results for a restaurant. Identify the leading and lagging measures, find the correlation matrix, and propose a cause-and-effect model using the strongest correlations.
15. The Excel file Automobile Options provides data on options ordered together for a particular model of automobile. Develop a market basket analysis using the XLMiner association rules procedure with the input parameters support = 6 and confidence = 80.
14. For the PC Purchase Data, identify association rules with the following input parameters for the XLMiner association rules procedure:a. support = 3; confidence = 90%b. support = 7; confidence = 90%c. support = 3; confidence = 70%d. support = 7; confidence = 70%Compare your results with those in
13. The Excel file Credit Risk Data provides a database of information about loan applications, along with a classification of credit risk in column L. Convert the categorical data into numerical codes as appropriate. Then apply logistic regression to classify training and validation data sets and
12. The Excel file Credit Risk Data provides a database of information about loan applications along with a classification of credit risk in column L. Convert the categorical data into numerical codes as appropriate. Then apply discriminant analysis to classify training and validation data sets and
11. The Excel file Credit Risk Data provides a database of information about loan applications along with a classification of credit risk in column L. Convert the categorical data into numerical codes as appropriate. Then apply the k-NN algorithm to classify training and validation data sets and
10. Use logistic regression to classify the new data in the Excel file Modified Credit Decisions using only credit score and years of credit history as input variables.
9. Use discriminant analysis to classify the new data in the Excel file Modified Credit Decisions using only credit score and years of credit history as input variables.
8. Use the k-NN algorithm to classify the new data in the Excel file Modified Credit Approval Decisions using only credit score and years of credit history as input variables.
7. Cluster the records in the Excel file Ten Year Survey. Create up to five clusters and analyze the results to draw conclusions about the survey.
6. Apply cluster analysis to the Excel file Sales Data, using the input variables Percent Gross Profit, Industry Code, and Competitive Rating. Create four clusters and draw conclusions about the groupings.
5. Apply cluster analysis to the numerical data in the Excel file Credit Approval Decisions.Analyze the clusters and determine if cluster analysis would be a useful classification method for approving or rejecting loan applications.
4. For the Colleges and Universities data, use XLMiner to find four clusters using each of the other clustering methods (see Figure 12.5); compare the results with Example 12.1.
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