Bangs Leisure Chairs produces three types of handcrafted outdoor chairs that are popular for beach, pool, and patios: sling chairs, Adirondack chairs, and hammocks. The unit profit for these products is $40, $100, and $90, respectively. Each type of chair requires cutting, assembling, and finishing. The owner is retired and is willing to work six hours/day for five days/week, so has 120 hours available each month. He does not want to spend more than 50 hours each month on any one activity (that is, cutting, assembling, and finishing). The retailer he works with is certain that all products he makes can easily be sold. Sling chairs are made up of ten wood pieces for the frame and one piece of cloth. The actual cutting of the wood takes 30 minutes. Assembling includes sewing of the fabric and the attachment of rivets, screws, fabric, and dowel rods, and takes 45 minutes. The finishing stage involves sanding, staining, and varnishing of the various parts and takes one hour. Adirondack chairs take two hours for both the cutting and assembling phases, and finishing takes one hour. For hammocks, cutting takes 0.4 hour; assembly takes three hours; and finishing also takes one hour. How many of each type of chair should he produce each month to maximize profit? a. Identify the decision variables, objective function, and constraints in simple verbal statements. b. Mathematically formulate a linear optimization model.
> Obtain the Solver Sensitivity Report for the Hal Chase portfolio optimization model. Explain how to interpret the Lagrange multipliers for the constraints.
> Figure 15.39 shows the Solver Sensitivity Report for the Markowitz portfolio model. a. Explain how to interpret the Lagrange multiplier value for the target portfolio return. b. Suppose the target return is increased from 10% to 11%. How much is the mini
> For the nonlinear pricing decision model, suppose that the company wants to keep the price at a maximum $300. Note that the solution in Figure 14.19 will no longer be feasible. Modify the spreadsheet model to include a constraint on the maximum price and
> For the Hansel Corporation, obtain the Solver Sensitivity Report and use it to answer the following: a. A labor strike in India leads to a shortage of 20,000 units of additive C. What should the production manager do? b. Management is considering raising
> Apply the Advanced Filter to the Credit Risk Data (Base Data worksheet) to find the following: a. All new car loans obtained for single females. b. All furniture loans obtained for single individuals who rent. c. All education loans obtained by unskilled
> For the ColPal Products scenario, use the spreadsheet model to answer the following question by changing the parameters and re-solving the model. Answer each question independently relative to the original problem. a. Suppose that the exposure for TV a
> For Problem (Shafer Office Supplies), obtain the Solver Sensitivity Report and answer the following questions: a. Suppose that 500 units of extra supply are available (and that the cost of this extra capacity is a sunk cost). To which distribution center
> StraitCarrier and SunShipping, obtain the Solver Sensitivity Report and write a short memo to the directors of both the companies explaining your results.
> For Dara’s investment situation, obtain the Solver Sensitivity Report and interpret the information, making recommendations that Dara might consider for her portfolio.
> For Susan’s cake recipe scenario, obtain the Solver Sensitivity Report and write a short memo to Susan explaining the sensitive information in language that she can understand.
> Model and solve an optimization model for planting corns and carrots. Using the Solver Sensitivity Report, answer the following questions, explaining what information you used in Sensitive Report. a. What impact will changing the required minimum number
> Model and solve an optimization model for the Morton Supply Company. Obtain the Solver Sensitivity Report for your solution, and clearly explain all the key information in language that the production manager would understand.
> Bangs Leisure Chairs. The Solver Sensitivity Report for the optimal solution is shown in Figure 15.38. Clearly explain the information it provides.
> Dion must now purchase at least 5 units of Product A, 15 units of Product B, and 10 units of Product C to fulfill his demand. Use Solver to find an optimal solution and compare the Solver solution with the result you found earlier using the Solver Sensit
> Use the Sensitivity Report for the Camm Textiles scenario (Figure 15.37) to answer the following: a. Explain the reduced cost (0.14) for Fabric 2 Purchased in terms of the original data, and why it makes sense. b. Explain the shadow price for the dobbie
> Use the Excel file Credit Risk Data that was introduced in this chapter to perform the following activities: a. Compute the combined checking and savings account balance for each record in the Base Data worksheet. Then sort the records by the number of m
> Obtain the Solver Sensitivity report for the GAC transportation model. a. What must the unit shipping cost be to make it attractive to ship from Marietta to Cleveland instead of from Minneapolis? b. Why are the Allowable Increases for all demand constrai
> For the Valencia Products scenario, use the spreadsheet model to answer the following questions by changing the parameters and re-solving the model. Answer each question independently relative to the original problem. a. If the unit profit for SpeedBuste
> 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 unif
> Mix&Match Ltd., a small fertilizer manufacturer, produces two active formulae of fertilizer mixtures. The mixtures must contain a minimum quantity of four different nutrients: 45 grams of nutrient A, 25 grams of nutrient B, 10 grams of nutrient C, an
> Steven is a 20-year-old male who suffers from chronic malnutrition. His doctor advices him to follow a dietary plan that will help him recover efficiently. He would need to take at least 400 grams of protein, 350 milligrams of iron, 300 milligrams of zin
> Panasonic Corporation is a multinational electronics corporation headquartered in Osaka, Japan. In the face of tight competition in the electronics industry and to meet the high level of demand, Panasonic’s factory operates 24 hours a d
> ACTN Partners, an accounting firm, recently received project offers from three different companies, A, B, and C, to analyze and prepare accounting data. The companies need the analysis and report to be completed in a month’s time. Due t
> For the Brewer Services scenario described in this chapter, suppose that five permanent employees are hired. Find an optimal solution to minimize the number of part-time employees needed.
> Suppose the distances that Mohan Raja, a mechanical technician for Canon who repairs and services photocopy machines, travels between five different companies that rent photocopy machines from Canon are as follows: Set up and solve a traveling salesperso
> An IT support group at Thomson State College has seven projects to complete. The time each will take and project deadlines (both given in number of days) are shown next. a. Sequence the projects to minimize the average lateness. b. Sequence the projects
> Filter the data in the Cereal database to obtain the cereals that are of type C. What are the average calories and total sales for this type of cereal?
> Dilan is a property investor. Recently he has been interested to invest in three different types of property: a shoplot, a condominium, and a double-story house. The shoplot is a high-risk investment, often resulting in heavy losses but occasionally comi
> ToyDoc is a major toy manufacturer. Its financial advisor is analyzing the effect of the direct material cost of plastic used to make the toys on profits earned for two of their main products. These data are available in the Excel file ToyDoc. Suppose th
> Many manufacturing situations, for example, the production of such large and complex items as aircraft or machines, exhibit a learning effect in which the production time per unit decreases as more units are produced. This is often modeled by a power cur
> We noted that the least-squares coefficients in a regression model are found by minimizing the sums of squares of the errors, as given in equation. This is a nonlinear optimization problem. Using the Home Market Value data, set up a spreadsheet model to
> ElectroMart wants to identify a location for a warehouse that will ship to five retail stores. The coordinates and annual number of truckloads are given here. Develop and solve a model to find the best location, assuming that straight-line distances can
> A franchise of a chain of H&M, a Swedish multinational clothing retail company, wants to determine the best location to attract customers from three shopping malls. The coordinates of the three shopping malls are as follows: The population shop at On
> In the hotel pricing problem, suppose that the hotel is considering adding suites to its room mix. Based on an analysis of local competitors, suites can sell for a rate of $180, and they expect to sell 20 per day to business travelers. The price elastici
> For the pricing decision model, suppose that the company wants to keep the price at a maximum of $500. Note that the solution in Figure will no longer be feasible. Modify the spreadsheet model to include a constraint on the maximum price and solve the mo
> Intel, the largest semiconductor manufacturing company in the world, sells two major types of computer chips, type A and type B. The sales of these two chips are not independent of each other (in economics, we call these substitutable products because if
> The demand for organic chicken meat is quite sensitive to price. Typically, there is an inverse relationship between its demand and price; when price decreases, demand increases and vice versa. One major organic chicken supplier found that when the price
> Use Excel’s filtering capability in the Car database to extract a. all Japanese cars. b. all cars having more than 400 horsepower. c. all cars having less than 8 cylinders and weighing more than 3,500 kilograms.
> A manufacturer of kitchen appliances is preparing to set the price on a new blender. Demand is thought to depend on the price and is represented by the model D = 2,000 - 3P The accounting department estimates that the total costs can be represented by C
> Foodpanda is an online food delivery brand headquartered in Berlin, Germany, and operating in over 10 countries. It is establishing a new business to serve customers in Selangor, a state on the west coast of Peninsular Malaysia, covering cities like Peta
> SnapHouse is a local property agents’ team who make profit on renting and selling residential units. Currently, they are focusing on a newly developed residential area and are helping the developer sell new units at an average price of $400,000 per unit.
> 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 a
> Rita is a part-time business student who works full time and is socially very active. She recognizes the challenge of eating a balanced diet and wants to minimize cost while meeting her basic nutritional requirements. Based on some research, she found th
> Puma SE, a German multinational company that manufactures athletic and casual apparel, footwear, and accessories, is launching their new jersey for the upcoming soccer season. They need to determine which famous soccer players to choose to be ambassadors
> A local university is considering offering five new programs for the next academic year. As a result, the university’s board of management needs to determine which programs to fund. Each program requires different facilities as well as
> Timberland Co. is an automobile manufacturer based in Australia. It has four plants and six sales depots. Timberland produces 165 cars and receives a demand for 86 cars. Since production is more than demand, the company wants to shut down some plants. Th
> Solve Valencia Products to ensure that the number of units produced is integer-valued. How much difference is there between the optimal integer solution objective function and the linear optimization solution objective function? Would rounding the contin
> FlowerAurora, a florist and gifts shop, prepares three types of flower bouquets to sell on the convocation day at a local university. The bouquets are made from four types of flowers: Gypsophila, gerberas, roses, and tulips. The number of stalks of each
> Conduct a Pareto analysis for the number of minutes that flights are late in the Global Airline Data Excel file. Interpret the results.
> A paper mill produces three grades of paper: X, Y, and Z. The mill has a budget of €100,000 to invest in the production of these three different types of paper. The cost per ton and expected profit over the next two years is given in the
> MK Manufacturing produces compressor and turbine blades for jet engines. The blades are manufactured from an alloy that is a mix of aluminum and titanium. Sheaths are part of the assembly that keep the compressor blades lightweight and are made from stee
> WoodFurni is a furniture manufacturer company that produces three main types of furniture: chairs, tables, and wardrobes. All three products require design and execution, and grinding and polishing before they can be shipped to customers. The following d
> 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-gallo
> Starbucks coffee company uses three types of cup sizes for selling its bestseller drink Mocha Frappuccino: Tall, (8 ounces), Grande (12 ounces), Venti (16 ounces), which have unit profits of $0.60, $0.65, and $0.75, respectively. The projected monthly sa
> Suppose that David Samuel wants to invest in three company shares: APPL, FB, and IBM. He decides to do some market research before he invests his money in these shares. The following table provides information about the share units per transaction for ea
> Joan Weasley receives a reward bonus semi-annually from her company: $3,000 on 1st June and $3,500 on 1st December. She must pay $1,500 as an insurance installment for each of the January, April, July, and October quarters of the year. Payments are due o
> 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. R&R employs four peop
> FujiFarm produces four types of vegetables with variable costs of $2.80, $3.54, $1.07, and $2.23 per acre. Due to an increment in the cost of fertilizers, the variable cost of each of the vegetables will increase by 3% at the beginning of next month. Dem
> The Excel file Retail Survey provides data about customers’ preferences for denim jeans. Use PivotTables and slicers to draw conclusions about how preferences differ by gender and age group and summarize your results in a brief memo.
> The background for this case was introduced in Chapter 2. For this part of the case, summarize the numerical data using frequency distributions and histograms, cross-tabulations, PivotTables, and descriptive statistics measures; find proportions for cate
> 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 plasti
> 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 n
> Box 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 produc
> StraitCarrier and SunShipping are two logistics companies based in Malaysia. Both companies offer shipment services to four different neighboring countries, and the cost of shipping one container from Malaysia to the respective countries is given in the
> The Little Investment Advisors problem and illustrated scaling issues. In answering the following questions, be sure to scale the model appropriately. a. How would the results in Figure 13.26 change if there is a limit of $100,000 in each fund? b. What i
> DwiFurni, a furniture store, is conducting a sale at a local market. The store outsources its furniture production and has a budget of $30,000 for procurements costs. The table Data for Problem 33 shows the top four furniture items selling at the store w
> Boris’ 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 te
> The Social Health Group is a nonprofit organization that conducts health talks for the local public. The organization conducts these talks at two different venues: Iron Age Hall and Virtual Town Amphitheatre. For the upcoming year, seven talks will be he
> Review the portfolio allocation model in this chapter. Identify the decision variables, objective function, and constraints in simple verbal statements, and mathematically formulate the linear optimization model.
> Sweet Tea markets three blends of tea: English breakfast, jasmine, and genmaicha. The firm uses tea leaves from its sources in India, China, and Japan. Net profit per pound for each blend is: $0.60 for English breakfast, $0.30 for jasmine tea, and $0.40
> The Excel file MBA Motivation and Salary Expectations provides data on students’ pre-MBA salary and post-MBA salary expectations. Define range names for each of these ranges and then use the range names in formulas to find the expected salary increase fo
> Ascent Constructions builds four different types of residential spaces: flats, condominiums, single-story houses, and double-story houses. Each type requires basic development in five different units: a. How many of each type of residential space should
> Most cake recipes have the basic ingredients of eggs, oil, flour, and milk. Susan just baked a cake, using 85% of the eggs, 73% of the oil, 78% of the flour, and 92% of the milk that she bought, by following the instructions from a recipe book that state
> For the investment situation, 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.
> Classify the following descriptions of constraints as bounds, limitations, requirements, proportional relationships, or balance constraints: a. A production line is sufficiently meeting its customers’ orders. b. The total amount of money available to inv
> For the ColPal model, 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.
> For the Valencia Products model, 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.
> A farmer plans to plant both corn and carrot on a 100-hectare land. To meet his requirements, he must plant at least 20 hectares with corn and 35 hectares with carrot. In order to maximize his profit, he wants to plant more corn than carrot; however, wit
> Implement the linear optimization model that you developed for the Flower Aurora shop on a spreadsheet and use Solver to find an optimal solution. Interpret the Solver Answer Report and identify the binding constraints. [Note: Answers may be in integers
> Implement the linear optimization model that you developed for Bangs Leisure Chairs on a spreadsheet and use Solver to find an optimal solution. a. Interpret the Solver Answer Report, identify the binding constraints, and verify the values of the slack v
> Dion’s Décor shop has three bestseller products. Dion has a budget of $2,500 to purchase these products from an outstation wholesale warehouse. The cost and the profits made from the sale of each of these products are given
> Use PivotTables to find the number of loans by different purposes, marital status, and credit risk in the Excel file Credit Risk Data (Base Data worksheet).
> Implement the linear optimization model that you developed for Burger Office Equipment on a spreadsheet and use Solver to find an optimal solution. Interpret the Solver Answer Report, identify the binding constraints, and verify the values of the slack v
> Implement the linear optimization model that you developed for ColPal Products on a spreadsheet and use Solver to find an optimal solution. Interpret the Solver Answer Report, identify the binding constraints, and verify the values of the slack variables
> Implement the linear optimization model that you developed for Valencia Products on a spreadsheet and use Solver to find an optimal solution. Interpret the Solver Answer Report, identify the binding constraints, and verify the values of the slack variabl
> Malloy Milling grinds calcined alumina to a standard granular size. The mill produces two different size products from the same raw material. Regular grind can be produced at a rate of 10,000 pounds per hour and has a demand of 400 tons per week with a p
> Suggest additional generic examples of linear optimization models in the format based on your work experience, personal interests (hobbies, etc.), or information found in business articles.
> A government body is putting a large project out for low bid. Bids are expected from eight contractors and will have a normal distribution with a mean of $4.2 million and a standard deviation of $0.27 million. Devise and implement a sampling experiment s
> A formula in financial analysis is the following: Return on equity = net profit margin * total asset turnover * equity multiplier. Suppose that the equity multiplier is fixed at 3.5, but that the net profit margin is normally distributed with a mean of 3
> Historical data shows that the birth weight of a random pool of 3,226 newborn babies with a mean of 3.39 kg and a standard deviation of 0.55 kg per baby, is normally distributed, but never more than 6 kg. Assuming that each newborn baby is independent of
> The exponential distribution of the amount of time a car battery lasts has a mean of 4 years. Generate 20 random variates from this distribution as whole Numbers.
> The time required to play the Pandemic board game is uniformly distributed between 45 and 60 minutes. Use formula to obtain a sample of 50 outcomes and compute the mean, minimum, maximum, and standard deviation.
> Construct PivotTables showing the counts of region versus social media platform market share, and tablet versus mobile device usage in Asia in the Excel file Social Media Market share. What might you conclude from this analysis?
> In many queueing situations, the time between arrivals and service times are assumed to have exponential distributions. Modify the car wash model to simulate a queueing system with an exponential arrival rate of l = 2 customers/minute (that is, a time be
> For the car wash simulation model, use data tables to find the distributions for the maximum number in the queue, maximum waiting time, average waiting time per customer, and total idle time. Use 100 trials for each.
> The Miller-Orr model in finance addresses a firm’s problem of managing its cash position by purchasing or selling securities at a transaction cost in order to lower or raise its cash position. That is, the firm needs to have enough cash on hand to meet i
> E-Globex is a moneychanger headquartered in Kuala Lumpur, Malaysia. It quotes the current US Dollar to Malaysian Ringgit exchange rate to be RM4.1740 for every 1 US Dollar. The daily price changes over the last 30 days are analyzed, resulting in the foll
> A front office receptionist of a given company answers the incoming calls on multi-line telephones. The number of calls successfully attended by the receptionist within each 5-minute period is recorded, resulting in the following frequency distribution:
> In Jennifer Bellin’s leadership conference project, suppose that the activity times are uncertain. Estimated ranges for these times are shown in the table below. Develop a spreadsheet simulation model to find the distribution of the pro
> DemiGod Shipping Company forecasts a 10% increase in its sales over the year 2019. Its assets and liabilities, at the end of 2018, amount to $20 billion and $7 billion respectively. Sales for this period were $25 billion, earning a 3% profit margin. The
