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mathematics
numerical analysis

Questions and Answers of Numerical Analysis

Compute the temperature distribution for the L-shaped plate in Figure.
The Poisson equation can be written in three dimensions asSolve for the distribution of temperature within a unit cube with zero boundary conditions and f = -10. Employ ∆x = ∆y = ∆z 1/6.
Use MATLAB or Mathcad to develop a contour plot with flux arrows for the Excel solution from Prob. 31.9.Prob.31.9.
Use a software package to solve for the temperature distribution of the L-shaped plate in Fig. P29.18. Display your results as a contour plot with flux arrows.Fig.P29.18.
A version of the Poisson equation that occurs in mechanics is the following model for the vertical deflection of a bar with a distributed load P(x):where Ac = cross-sectional area, E = Young’s
Develop a user-friendly program to model the steady-state distribution of temperature in a rod with a constant heat source using the finite-element method. Set up the program so that unequally spaced
Use MATLAB or Mathcad to develop a contour plot with flux arrows for the Excel solution from Prob. 31.7.
Use Excel to model the temperature distribution of the slab shown in Fig. P31.9. The slab is 0.02 m thick and has a thermal conductivity of 3 W/(m ∙ °C).Fig .P31.9.
Use Poisson's equation to compute the electric potential over a unit square (1 × 1) plate with zero voltage at the edges and point charge sources of ρv/ε (0.7, 0.7) = 1 and pv/ε (0.3, 0.3) = -1.
The displacement of a uniform membrane subject to a tension and a uniform pressure can be described by the Poisson equationSolve for the displacement of a 1-cm-square membrane that has P/T = 0.6/cm
The four short cases we have analyzed in this chapter (Retirement Planning, Draft TV Commercials, Icebergs for Kuwait, and Racquetball Racket) are reproduced with full details toward the end of this
The Boeing Company faces a critical strategic choice in its competition with Airbus Industries for the long-haul flight segment: Should it design and build a super-747 model that can carry 550
The Red Cross provides about 40 percent of the replacement blood supply for the United States. The available donor base has been shrinking for years, and although increased advertising has kept Red
Your client is the planning office of a major university. Part of the job of the planning office is to forecast the annual donations of alumni through the university's long-established giving
Congress is considering a new law that will grant amnesty to the roughly 13 million illegal aliens in the United States. Under this law, anyone who has entered the country illegally in the past can
Sketch graphs for the relationships described in each of the following problems and select one or more of the families of functions discussed in Section 2.4.4 to represent it.1. The relationship
Refer to the XYZ Company case. Design a spreadsheet that will allow an analyst to predict the month in which the cash balance falls below zero, signaling a need to borrow money. The following
Refer to the Medical Supplies for Banjul case. Design a spreadsheet that will enable you to request the required funds from your team's finance officer, order supplies from the home office, and
Refer to the Reid's Raisins case. Design a spreadsheet that will allow the firm to project profit for base-case conditions; the open market grape price is $0.30. The following exercises refer to the
Refer to the Big Rig Rental Company case. Design a spreadsheet that will allow the firm to determine the Net Present Value of cash flows over the five-year period.The following exercises refer to the
Refer to the Flexible Insurance Coverage case. Design a spreadsheet that will allow an individual employee with estimated annual medical expenses of $400 to compare the total expenses under each
Refer to the Snoey Software Company case. Design a spreadsheet that will determine the annual profit when the prices for the Educational, Large-Scale, and Professional versions are $100, $300, and
Refer to the Cox Cable and Wire Company case. In the role of Meredith, design a spreadsheet with which to find a machine schedule and a corresponding inventory and shipment schedule that meets
Refer to the BMW Company case. Design a spreadsheet that will allow the firm's managers to estimate what percentage of the firm's net income 10 years into the future will be devoted to disposal of
Refer to the XYZ Company case. From the corresponding exercise in Chapter 3, review the design of a spreadsheet that will allow an analyst to predict monthly cash needs and profitability for the
a. The population figures will show that there are 3,000 children, 2,500 teenagers, 500 seniors, and 9,000 other adults in the population. If there were no stock on hand, what amount would be
Refer to the Reid's Raisins case. From the corresponding exercise in Chapter 3, review the design of a spreadsheet that will allow the firm to determine how many grapes to buy under contract and how
a. What is the Net Present Value of the firm's cash flows over the five-year period? b. Construct a tornado chart for the analysis in (a). List the relevant parameters in descending order of their
a. Consider the case of a single employee with estimated annual expenses of $400. Which plan is the cheapest? What is the total annual cost associated with this plan?b. For the analysis in (a),
a. Consider a recommendation that the prices for the Educational, Large-Scale, and High-Speed versions should be $75, $275, and $475, respectively. What annual profit would these prices achieve?b.
Refer to the Cox Cable and Wire-Company case. In the role of Meredith, design a spreadsheet that will evaluate the profitability of any particular production and delivery schedule. a. Find a machine
a. What percentage is predicted for 1999, assuming there are no changes in trends and policies?b. How does the percentage change as a function of BMW's market share in 1999? (Consider a range from 5
The database Dish.xlsx contains a transaction history describing more than 4,000 purchases of detergent at a number of stores in a grocery chain over a period of several weeks.a. How many records are
The database Income.xlsx‡ contains average personal income data for a number of states over the years 1929-1999.a. How many records are in this database?b. How many fields are in this database?c.
The database Tissue.xlsx contains a transaction history describing more than 3,700 purchases of facial tissues at a number of stores in a grocery chain over a period of several weeks.a. How many
The database Population.xlsx contains data on the populations of the 50 states from 1990 to 1999. a. How many records are in this database? b. How many fields are in this database? c. Are there any
The database Applicants.xlsx contains a description of an MBA applicant pool.a. How many records are in this database?b. How many fields are in this database?c. W hat decision was made on the top
The database Boston Housing.xlsx* contains demographic, environmental, and housing data on a number of towns in the Boston area. a. How many records are in this database? b. How many fields are in
The database Universal Bank.xlsx*** contains information on a large number of current bank customers. a. How many records are in this database? b. How many fields are in this database? c. How many
The database Book Club.xlsx‡ contains data on a number of current customers of a direct-mail book club.a. How many records are in this database?b. How many fields are in this database?c. How many
Consider the example of the town of Lincoln, which was analyzed using a multiplicative model in Figure 7.14. Repeat the forecasts using the additive model, with the same smoothing constants.FIGURE
The operations manager at a manufacturing facility is about to begin an energy-efficiency initiative. As this program begins, it will be helpful to have benchmark data on energy use, in order to
Consider the stylized example of Figure 7.3, in which there is a jump in the mean value. Using the same worksheet as a template, enter the exponential smoothing calculations for these periods. Assume
Brad's Burritos provides a simple set of lunch offerings in a college town. The shop has recently decided to implement a forecasting system and is testing the use of exponential smoothing methods.
Garish Motors sells new and used automobiles. Sales of new cars over the past 50 weeks are given in the following table (week 50 is the most recent).a. Compute a forecast for sales next week by using
Data covering the most recent 30 days are given in the following table for the price per gallon of regular gasoline at a local station.a. Compute a forecast for the next day's price by using a 3-day
Contributions to the disaster relief fund for a national charity average around $1 million a month and do not exhibit trend or seasonal effects. Data on the most recent 12 months is given in the
Consider the example of Figure 7.7, in which the smoothing constant was taken to be Î± = 0:2. Repeat the calculations for smoothing constants between 0.1 and 0.9, in steps of 0.1.FIGURE
Consider the example of the new product at Curtis Distributors, which was analyzed using Holt's method in Figure 7.12. Repeat the forecasts using one smaller value of a than the value of 0.2 used in
Consider the stylized example in Figure 7.13. Repeat the forecasts using the additive model with trend, using the same smoothing constants.FIGURE 7.13 Stylized Model with Trend and Cyclic
Return to the Kilroy Paper Company example introduced in this chapter. Upon further consideration, the logistics manager points out that the trucks do not make an equal number of trips to the various
Oliveira Office Supply has a large retail system consisting of twelve stores spread around the country, often in direct competition with Kilroy. However, managers at Oliveira have decided to use two
Campbell Motors is an auto dealership that specializes in the sale of station wagons and light trucks. Because of its reputation for quality and service, Campbell has a strong position in the
A regional beer distributor has $100,000 to spend on advertising in four markets, where each market responds differently to advertising. Based on observations of each market's response to several
A well-known charity is interested in conducting a television campaign to solicit contributions. The campaign will be conducted in two metropolitan areas. Past experience indicates that, in each
The Bogard Corporation produces three types of bookcases, which it sells to large office supply companies. The production of each bookcase requires two machine operations, trimming and shaping,
Hill-O-Beans Coffee Company blends four component beans into three final blends of coffee: one is sold to luxury hotels, another to restaurants, and the third to supermarkets for store label brands.
You are the Director of the Computer Center for Gaillard College and responsible for scheduling the staffing of the center, which is open from 8 a.m. until midnight. You have monitored the usage of
A construction contractor is responsible for a project with seven key tasks. Some of the tasks can begin at any time, but others have predecessor tasks that must be completed previously. The
The facilities manager at Oxbridge University is planning to apply fertilizer to the grass in the quadrangle area in the spring. The grass needs nitrogen, phosphorus, and potash in at least the
The Andrews Apple Products Company purchases apples from local growers and makes applesauce and apple juice. It costs $0.80 to produce a jar of applesauce and $0.60 to produce a bottle of apple
The Auto Company of America (ACA) produces four types of cars: subcompact, compact, intermediate, and luxury. ACA also produces trucks and vans. Vendor capacities limit total production capacity to
The Schutzberg Brewery has received an order for 1,500 gallons of 3-percent beer (that is, 3 percent alcoholic content). This is a custom order because Schutzberg does not produce a 3-percent
A sudden increase in the demand for smoke detectors has left Acme Alarms with insufficient capacity to meet demand. The company has seen monthly demand from its retailers for its electronic and
An oil company produces three brands of oils: Regular, Multi grade, and Supreme. Each brand of oil is composed of one or more of four crude stocks, each having a different viscosity index. The
The Calcio Coal Company produces coal at four mines and ships it to four power plants (P1-P4). The cost per ton of producing coal and the production capacity (in tons) for each mine are known. The
Coastal Refining Company operates a refinery with a distillation capacity of 12,000 barrels per day. As a new member of Coastal's management team, you have been given the task of developing a
A manufacturer of nylon carpets produces rolls of carpeting at four factories and ships them to distributors in five locations The following table shows the capacities at the factories and the
The Texas Electronics Company (TEC) is contemplating a research and development program encompassing eight major projects. The company is constrained from embarking on all projects by the number of
Oriental Airlines is considering a capital expansion in which it will purchase new aircraft for its Pacific runs. Oriental is looking at the purchase of Boeing B797s, Airbus A450s, and Lockheed
Poly Products sells packaging tape to industrial customers. All tape is sold in 100-foot rolls that are cut in various widths from a master roll, which is 15 inches wide. The product line consists of
Universal Technologies, Inc. has identified two qualified vendors with the capability to supply certain of its electronic components. For the coming year, Universal has estimated its volume
In the previous problem, suppose that vendor A provides a new price-discount schedule for component 3. This one is an "incremental" discount, as opposed to an "all-units" discount, as follows: Unit
Southeastern Foods has hired you to analyze their distribution-system design. The company has 11 distribution centers, with monthly volumes as listed below. Seven of these sites can support
You are organizing rides for a group of campers going on an all-day, off-site trip. You have lined up some drivers, and your problem is to assign campers to drivers. The drivers and the capacities of
A set of ten jobs must be scheduled at an integrated machining center that performs a number of metal-cutting operations on components for complex assemblies. These jobs and their processing times
During the next 8 months, Metropolis Power Company forecasts the demands shown in the table below (measured in thousands of kwh):Power will be supplied from the four generating facilities, GF1- GF4.
National Metals Company (NMC) manufactures titanium shafts. Its equipment is capable of producing shafts in ten lengths, reflecting different settings on its machinery. These lengths are 32 cm to 50
A set of ten jobs must be scheduled at an integrated machining center that performs a number of metal-cutting operations on components for complex assemblies. These jobs and their processing times
Midwest Parts Supply (MPS) is a fabricator of small steel parts that are sold as components to manufacturers of electronic appliances and medical equipment. In the MPS fabrication department, steel
A painting operation is scheduled in blocks, where each block involves painting products with a particular color. Cleaning time is required in between each pair of blocks so that the equipment can be
Crawford Labs has increased its profitability dramatically by using models to allocate its sales force among the company's major drugs. To guide that effort, a nonlinear sales-response curve is
Recent graduate and world traveler Alastair Bor is planning a European trip. He is influenced by his curiosity about urban culture in the EU and by his study of international relations while he was
In early 1984, Pennzoil and Getty Oil agreed to the terms of a merger. Before any formal documents could be signed, however, Texaco offered Getty Oil a substantially better price, so Gordon Getty,
Liedtke's advisors suggest that Texaco has more options in the face of Pennzoil's $5 billion counteroffer than simply to refuse or accept. In particular, they might counteroffer, probably with an
The Taiwanese government recently announced that they would begin construction of a high-speed rail system linking the northernmost city of Taipei to the southernmost city, Tai-Nan. This high-speed
Gamma's objective is to select the bid that maximizes its expected profit.a. What is the optimal bid for Gamma to make? b. What is the expected profit associated with the optimal bid in part (a)? c.
In the early 1980s, New England Electric System (NEES) was deciding how much to bid for the salvage rights to a grounded ship, the SS Kuniang. If the bid were successful, the ship could be repaired
You have been asked to evaluate the following investment opportunity. A small firm is available for purchase at an initial cost of $150,000, to be paid to the current owner in equal installments over
As the manager of credit card services at Bank of Hanover (BOH), you're aware that the average profitability of a credit card customer grows with the number of years they have used the credit card.
A simple model is sometimes used in order to illustrate the production-scheduling maxim, "balance flow, not capacity." Consider a factory that consists of three workstations where each customer order
Two partners have decided to sell the manufacturing business they have been running. They have lined up five prospective buyers and have hired a consultant to help them with the bidding and the sale.
A sealed-bid auction is going to be held in the near future for Medex Pharmaceuticals. You represent one of two companies expected to enter bids. The basic data available to your firm consist of an
A given stock is currently priced at $100. Historically, its annual return has been 12 percent with a standard deviation of 15 percent. Build a spreadsheet simulation model for the stock price, using
Alpha Airlines has ordered a new fleet of DC- 717s. At this stage of the contract, Alpha's operations manager must specify the seating configuration on the aircraft that will be used on the
An electric utility currently operates ten plants. The following table gives the fixed costs, variable costs, and capacities of each of these plants. Daily demand is highly uncertain, given by a
An architectural design firm is faced with a decision as to which projects to bid on for the coming year. Ten projects are available for which they are qualified. The following table lists the profit
You have been hired to estimate the value of the startup company Garcia, Ltd. Garcia has one product, which is expected to sell in the first year for $100. The price will grow in subsequent years by
A computer manufacturer sells its laptop model through a web-based distributor, who buys at a unit cost of $200 and sells at a unit price of $500. The product life cycle is so short that the
A small hotel has 50 rooms that rent for $105 per night and cost $45 to clean and prepare each night they are used. All rentals are by reservation and there is a 10 percent chance that an individual

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