New Semester Started Get 50% OFF Study Help! --h --m --s Claim Now

Question Answers

Textbooks

Find textbooks, questions and answers

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
mathematics
statistics

Introduction to Operations Research 10th edition Frederick S. Hillier, Gerald J. Lieberman - Solutions

Consider the following table of constraint coefficients for a linear programming problem.Show how this table can be converted into the form for multidivisional multitime period problems shown in Table 23.12 (with two linking constraints, two linking variables, and four subproblems in this case) by
Consider the Woodstock Company multitime period problem described in Sec. 23.4 (see Table 23.10). Suppose that the company has decided to expand its operation to also buy, store, and sell plywood in this warehouse. For the upcoming year, the relevant data for raw lumber are still as given in Sec.
Consider the airline company problem presented in Prob. 10.3-3. (a) Describe how this problem can be fitted into the format of the transshipment problem. (b) Reformulate this problem as an equivalent transportation problem by constructing the appropriate parameter table.
A student about to enter college away from home has decided that she will need an automobile during the next four years. Since funds are going to be very limited, she wants to do this in the cheapest possible way. However, considering both the initial purchase price and the operating maintenance
Without using xii variables to introduce fictional shipments from a location to itself, formulate the linear programming model for the general transshipment problem described at the end of Sec. 23.1. Identify the special structure of this model by constructing its table of constraint coefficients
Consider the following linear programming problem.Maximize Z = 2x1 + 4x2 + 3x3 + 2x4 + 5x5 + 3x6,subject toand xj ‰¥ 0, for j = 1, 2, . . . , 6. (a) Rewrite this problem in a form that demonstrates that it possesses the special structure for multidivisional problems. Identify the variables
Consider the following table of constraint coefficients for a linear programming problem:(a) Show how this table can be converted into the block angular structure for multidivisional linear programming as shown in Table 23.4 (with three subproblems in this case) by reordering the variables and
A corporation has two divisions (the Eastern Division and the Western Division) that operate semiautonomously, with each developing and marketing its own products. However, to coordinate their product lines and to promote efficiency, the divisions compete at the corporate level for investment funds
Use the decomposition principle to solve the Wyndor Glass Co. problem presented in Sec. 3.1.
Consider the following multidivisional problem:Maximize Z = 10x1 + 5x2 + 8x3 + 7x4,subject toand xj ‰¥ 0, for j = 1, 2, 3, 4. (a) Explicitly construct the complete reformulated version of this problem in terms of the pjk decision variables that would be generated (as needed) and used by
A cube has its six sides colored red, white, blue, green, yellow, and violet. It is assumed that these six sides are equally likely to show when the cube is tossed. The cube is tossed once. (a) Describe the sample space. (b) Consider the random variable that assigns the number 0 to red and white,
The number of orders per week, X, for radios can be assumed to have a Poisson distribution with parameter λ = 25. (a) Find P{X ≥ 25} and P{X = 20}. (b) If the number of radios in the inventory is 35, what is the probability of a shortage occurring in a week?
Consider the following game. Player A flips a fair coin until a head appears. She pays player B 2n dollars, where n is the number of tosses required until a head appears. For example, if a head appears on the first trial, player A pays player B $2. If the game results in 4 tails followed by a head,
The demand D for a product in a week is a random variable taking on the values of –1, 0, 1 with probabilities 1/8, 5/8, and C/8, respectively. A demand of – 1 implies that an item is returned. (a) Find C, E(D), and variance D. (b) Find E(eD2). (c) Sketch the CDF of the random variable D,
In a certain chemical process three bottles of a standard fluid are emptied into a larger container. A study of the individual bottles shows that the mean value of the contents is 15 ounces and the standard deviation is 0.08 ounces. If three bottles form a random sample, (a) Find the expected value
Consider the density function of a random variable X defined by(a) Find the CDF corresponding to this density function. (Be sure you describe it completely.) (b) Calculate the mean and variance. (c) What is the probability that a random variable having this density will exceed 0.5? (d) Consider the
A transistor radio operates on two 1 ½ volt batteries, so that nominally it operates on 3 volts. Suppose the actual voltage of a single new battery is normally distributed with mean 1 ½ volts and variance 0.0625. The radio will not operate “properly” at the outset if the voltage falls outside
The life of electric lightbulbs is known to be a normally distributed random variable with unknown mean μ and standard deviation 200 hours. The value of a lot of 1,000 bulbs is (1,000) (1/5,000) μ dollars. A random sample of n bulbs is to be drawn by a prospective buyer, and 1,000(1/5,000)
A joint random variable (X1, X2) is said to have a bivariate normal distribution if its joint density is given byfor €“ˆž (a) Show that E(X1) = Î¼X1 and E(X2) = ÏƒX2. (b) Show that variance (X1) = Ïƒ2X1, variance (X2) = Ïƒ2X2, and the
The joint demand for a product over 2 months is a continuous random variable (X1, X2) having a joint density given by(a) Find c. (b) Find FX1X2 (b1, b2), FX1 (b1), and FX2 (b2). (c) Find fX2|X1€“s(t).
Two machines produce a certain item. The capacity per day of machine 1 is 1 unit and that of machine 2 is 2 units. Let (X1, X2) be the discrete random variable that measures the actual production on each machine per day. Each entry in the table below represents the joint probability, for example,
Suppose the sample space „¦ consists of the four pointsw1, w2, w3, w4,and the associated probabilities over the events are given byDefine the random variable X1 by X1 (w1) = 1, X1 (w2) = 1, X1 (w3) = 4, X1 (w4) = 5, and the random variable X2 by X1 (w1) = 1, X2 (w2) = 1, X2 (w3) = 1, X2
Suppose that E1, E2, . . . , Em are mutually exclusive events such that E1 U E2, U . . .,Em = „¦; that is, exactly one of the E events will occur. Denote by F any event in the sample space. Note thatand that FE1, i = 1, 2, . . . , m, are also mutually exclusive. (a) Show that (b) Show
During the course of a day a machine turns out two items, one in the morning and one in the afternoon. The quality of each item is measured as good (G), mediocre (M), or bad (B). The longrun fraction of good items the machine produces is 1 2, the fraction of mediocre items is 1 3, and the fraction
The random variable X has density function f given by(a) Determine K in terms of Î¸. (b) Find FX(b), the CDF of X. (c) Find E(X). (d) Suppose
Let X be a discrete random variable, with probability DistributionAnd P(X = x2) = ¾. (a) Determine x1 and x2, such that E(X) = 0 and variance (X) = 10. (b) Sketch the CDF of X.
The life X, in hours, of a certain kind of radio tube has a probability density function given by(a) What is the probability that a tube will survive 250 hours of operation? (b) Find the expected value of the random variable.
The random variable X can take on only the values 0, ±1, ±2, and(a) Find the probability distribution of X. (b) Graph the CDF of X. (c) Compute E(X).
Let X be a random variable with density(a) What value of K will make fX(y) a true density? (b) What is the CDF of X? (c) Find E(2X €“ 1). (d) Find variance (X). (e) Find the approximate value of P{X€“bar > 0}, where X is the sample mean from a random sample of size n = 100 from
The distribution of X, the life of a transistor, in hours, is approximated by a triangular distribution as follows:(a) What is the value of a? (b) Find the expected value of the life of transistors. (c) Find the CDF, FX(b), for this density. Note that this must be defined for all b between plus and
Show that the structure function for a three-component system that functions if and only if component 1 functions and at least one of components 2 or 3 functions is given by
Follow the instructions of Prob. 25.4-1 when using the following network.(a) Find all the minimal paths and cuts. (b) Compute the exact system reliability, and evaluate it when pi = p = 0.90. (c) Find upper and lower bounds on the reliability, and evaluate them when pi = p = 0.90.
Consider the following network.Assume that each component is independent with probability pi of performing satisfactorily. (a) Find all the minimal paths and cuts. (b) Compute the exact system reliability, and evaluate it when pi = p = 0.90. (c) Find upper and lower bounds on the reliability, and
Suppose F is IFR, with μ = 0.5. Find upper and lower bounds on R(t) for (a)t = 1/4 and (b) t = 1.
A time-to-failure distribution is said to have a Weibull distribution if the cumulative distribution function is given by F(t) = 1 –e–tβ /ƞ , where ƞ, β > 0. Find the failure rate, and show that the Weibull distribution is IFR when β ≥ 1 and DFR when 0 < β ≤ 1.
Suppose that a system consists of two different, but independent, components, arranged into a series system. Further assume that the time to failure for each component has an exponential distribution with parameter θi, I = 1, 2. Show that the distribution of the time to failure of the system is
Consider a parallel system consisting of two independent components whose time to failure distributions are exponential with parameters Î¼1 and Î¼2, respectively (Î¼1 ‰ Î¼2). Show that the time to failure distribution of the system is
For Prob. 25.5-4, show that the time to failure distribution is IFRA.
Show that the structure function for a four-component system that functions if and only if components 1 and 2 function and at least one of components 3 or 4 functions is given by ɸ(X1, X2, X3, X4) X1 X2 max (X3, X4).
Find the reliability of the structure function given in Prob. 25.1-1 when each component has probability pi of performing successfully and the components are independent.
Find the reliability of the structure function given in Prob. 25.1-2 when each component has probability pi of performing successfully and the components are independent.
Consider a system consisting of three components (labeled 1, 2, 3) that operate simultaneously. The system is able to function satisfactorily as long as any two of the three components are still functioning satisfactorily. The goal is for the system to function satisfactorily for a length of time
Consider a system consisting of five components, labeled 1, 2, 3, 4, 5. The system is able to function satisfactorily as long as at least one of the following three combinations of components has every component in that combination functioning satisfactorily: (1) Components 1 and 4; (2) Components
Suppose that there exist three different types of components, with two units of each type. Each unit operates independently, and each type has probability pi of performing successfully. Either one or two systems can be built. One system can be assembled as follows: The two units of each type of
Follow the instructions of Prob. 25.4-1 when using the following network.Note that component 3 flows in both directions. (a) Find all the minimal paths and cuts. (b) Compute the exact system reliability, and evaluate it when pi = p = 0.90. (c) Find upper and lower bounds on the reliability, and
Follow the instructions of Prob. 25.4-1 when using the following network.(a) Find all the minimal paths and cuts. (b) Compute the exact system reliability, and evaluate it when pi = p = 0.90. (c) Find upper and lower bounds on the reliability, and evaluate them when pi = p = 0.90.
For each kind of queueing system listed in Prob. 17.3-1, briefly describe the nature of the cost of service and the cost of waiting that would need to be considered in designing the system.
Jake’s Machine Shop contains a grinder for sharpening the machine cutting tools. A decision must now be made on the speed at which to set the grinder. The grinding time required by a machine operator to sharpen the cutting tool has an exponential distribution, where the mean 1/μ can be set at
Consider the special case of model 2 where (1) any μ > λ/s is feasible and (2) both f (μ) and the waiting-cost function are linear functions, so that E(TC) = Crsμ + CwL,
Consider a harbor with a single dock for unloading ships. The ships arrive according to a Poisson process at a mean rate of λ ships per week, and the service-time distribution is exponential with a mean rate of μ unloadings per week. Assume that harbor facilities are owned by the shipping
Consider a queueing system with two types of customers. Type 1 customers arrive according to a Poisson process with a mean rate of 5 per hour. Type 2 customers also arrive according to a Poisson process with a mean rate of 5 per hour. The system has two servers, and both serve both types of
Reconsider Prob. 17.6-32. (a) Formulate part (a) to fit as closely as possible a special case of one of the decision models presented in Sec. 26.4. (Do not solve.) (b) Describe Alternatives 2 and 3 in queueing theory terms, including their relationship (if any) to the decision models presented in
Consider the formulation of the County Hospital emergency room problem as a preemptive priority queueing system, as presented in Sec. 17.8. Suppose that the following inputted costs are assigned to making patients wait (excluding treatment time): $10 per hour for stable cases, $1,000 per hour for
A certain queueing system has a Poisson input, with a mean arrival rate of 4 customers per hour. The service-time distribution is exponential, with a mean of 0.2 hour. The marginal cost of providing each server is $20 per hour, where it is estimated that the cost that is incurred by having each
Reconsider Prob. 17.6-10. The total compensation for the new employee would be $8 per hour, which is just half that for the cashier. It is estimated that the grocery store incurs lost profit due to lost future business of $0.08 for each minute that each customer has to wait (including service
The Southern Railroad Company has been subcontracting for the painting of its railroad cars as needed. However, management has decided that the company can save money by doing this work itself. A decision now needs to be made to choose between two alternative ways of doing this. Alternative 1 is to
Consider a factory whose floor area is a square with 600 feet on each side. Suppose that one service facility of a certain kind is provided in the center of the factory. The employees are distributed uniformly throughout the factory, and they walk to and from the facility at an average speed of 3
Follow the instructions of Prob. 26.3-1 for the following waiting-cost functions.(a)(b)
A certain large shop doing light fabrication work uses a single central storage facility (dispatch station) for material in process storage. The typical procedure is that each employee personally delivers his finished work (by hand, tote box, or hand cart) and receives new work and materials at the
Consider Alternative 3 (tool cribs in Locations 1 and 3) for the example illustrated in Fig. 26.9. Derive E(T) for the tool crib in Location 3 by using the probability density functions of X and Y directly for this tool crib.
Suppose that the calling population for a particular service facility is uniformly distributed over each area shown, where the service facility is located at (0, 0). making the same assumptions as in sec. 26.5, derive the expected round-trip travel time per arrival e(t) in terms of the average
A job shop is being laid out in a square area with 600 feet on a side, and one of the decisions to be made is the number of facilities for the storage and shipping of final inventory. The capitalized cost associated with providing each facility would be $10/hour. There are just four potential
Suppose that a queueing system fits the M/M/1 model described in Sec. 17.6, with λ = 2 and μ = 4. Evaluate the expected waiting cost per unit time E(WC) for this system when its waiting-cost function has the form (a) g(N) = 10N + 2N2. (b) h(W) = 25W + W3.
The production of tractors at the Jim Buck Company involves producing several subassemblies and then using an assembly line to assemble the subassemblies and other parts into finished tractors. Approximately three tractors per day are produced in this way. An in-process inspection station is used
The car rental company, Try Harder, has been subcontracting for the maintenance of its cars in St. Louis. However, due to long delays in getting its cars back, the company has decided to open its own maintenance shop to do this work more quickly. This shop will operate 42 hours per
A certain small car-wash business is currently being analyzed to see if costs can be reduced. Customers arrive according to a Poisson process at a mean rate of 15 per hour, and only one car can be washed at a time. At present the time required to wash a car has an exponential distribution, with a
The Seabuck and Roper Company has a large warehouse in southern California to store its inventory of goods until they are needed by the company’s many furniture stores in that area. A single crew with four members is used to unload and/or load each truck that arrives at the loading dock of the
Trucks arrive at a warehouse according to a Poisson process with a mean rate of 4 per hour. Only one truck can be loaded at a time. The time required to load a truck has an exponential distribution with a mean of 10/n minutes, where n is the number of loaders (n = 1, 2, 3, . . .). The costs are (i)
A company’s machines break down according to a Poisson process at a mean rate of 3 per hour. Nonproductive time on any machine costs the company $60 per hour. The company employs a maintenance person who repairs machines at a mean rate of μ machines per hour (when continuously busy) if the
The Hammaker Company’s newest product has had the following sales during its first five months: 5 17 29 41 39. The sales manager now wants a forecast of sales in the next month. (Use hand calculations rather than an Excel template.) (a) Use the last-value method. (b) Use the averaging method. (c)
Even when the economy is holding steady, the unemployment rate tends to fluctuate because of seasonal effects. For example, unemployment generally goes up in Quarter 3 (summer) as students (including new graduates) enter the labor market. The unemployment rate then tends to go down in Quarter 4
Look ahead at the scenario described in Prob. 27.7-3. Notice the steady trend upward in the number of applications over the past three years—from 4,600 to 5,300 to 6,000. Suppose now that the admissions office of Ivy College had been able to foresee this kind of trend and so had decided to use
Exponential smoothing with trend, with a smoothing constant of α = 0.2 and a trend smoothing constant of β = 0.3, is being used to forecast values in a time series. At this point, the last two values have been 535 and then 550. The last two forecasts have been 530 and then 540. The last estimate
The Healthwise Company produces a variety of exercise equipment. Healthwise management is very pleased with the increasing sales of its newest model of exercise bicycle. The sales during the last two months have been 4,655 and then 4,935. Management has been using exponential smoothing with trend,
The Pentel Microchip Company has started production of its new microchip. The first phase in this production is the wafer fabrication process. Because of the great difficulty in fabricating acceptable wafers, many of these tiny wafers must be rejected because they are defective. Therefore,
Transcontinental Airlines maintains a computerized forecasting system to forecast the number of customers in each fare class who will fly on each flight in order to allocate the available reservations to fare classes properly. For example, consider economy-class customers flying in midweek on the
Reconsider Prob. 27.7-15. The economy is beginning to boom so the management of Transcontinental Airlines is predicting that the number of people flying will steadily increase this year over the relatively flat (seasonally adjusted) level of last year. Since the forecasting methods considered in
Quality Bikes is a wholesale firm that specializes in the distribution of bicycles. In the past, the company has maintained ample inventories of bicycles to enable filling orders immediately, so informal rough forecasts of demand were sufficient to make the decisions on when to replenish inventory.
Reconsider the sales data for a certain product given in Prob. 27.5-4. The company’s management now has decided to discontinue incorporating seasonal effects into its forecasting procedure for this product because there does not appear to be a substantial seasonal pattern. Management also is
Follow the instructions of Prob. 27.7-18 for a product with the following sales history.
Sales of stoves have been going well for the Good-Value Department Store. These sales for the past five months have been 15 18 12 17 13. Use the following methods to obtain a forecast of sales for the next month. (Use hand calculations rather than an Excel template.) (a) The last-value method. (b)
You have been forecasting sales the last four quarters. These forecasts and the true values that subsequently were obtained are shown below.(a) Calculate MAD. (b) Calculate MSE.
Sharon Johnson, sales manager for the Alvarez-Baines Company, is trying to choose between two methods for forecasting sales that she has been using during the past five months. During these months, the two methods obtained the forecasts shown below for the company€™s most important
Three years ago, the admissions office for Ivy College began using exponential smoothing with a smoothing constant of 0.25 to forecast the number of applications for admission each year. Based on previous experience, this process was begun with an initial estimate of 5,000 applications. The actual
Ben Swanson, owner and manager of Swanson€™s Department Store, has decided to use statistical forecasting to get a better handle on the demand for his major products. However, Ben now needs to decide which forecasting method is most appropriate for each category of product. One category
Reconsider Prob. 27.7-4. Ben Swanson now has decided to use the exponential smoothing method to forecast future sales of washing machines, but he needs to decide on which smoothing constant to use. Using an initial estimate of 24, apply this method retrospectively to the 12 months of last year with
Reconsider Prob. 27.7-4. For each of the forecasting methods specified in parts (b), (c), and (d), use the corresponding procedure in the forecasting area of your IOR Tutorial to obtain the requested forecasts. Then use the accompanying graph that plots both the sales data and forecasts to answer
Management of the Jackson Manufacturing Corporation wishes to choose a statistical forecasting method for forecasting total sales for the corporation. Total sales (in millions of dollars) for each month of last year are shown below.(a) Note how the sales level is shifting significantly from month
Reconsider Prob. 27.7-7. For each of the forecasting methods specified in parts (b), (c), and (d) (with smoothing constants α = 0.5 and β = 0.5 as needed), use the corresponding procedure in the forecasting area of your IOR Tutorial to obtain the requested forecasts. Then use the accompanying
Choosing an appropriate value of the smoothing constant α is a key decision when applying the exponential smoothing method. When relevant historical data exist, one approach to making this decision is to apply the method retrospectively to these data with different values of α and then choose the
The choice of the smoothing constants α and β has a considerable effect on the accuracy of the forecasts obtained by using exponential smoothing with trend. For each of the following time series, set α = 0.2 and then compare MAD obtained with β = 0.1, 0.2, 0.3, 0.4, and 0.5. Begin with initial
Ralph Billett is the manager of a real estate agency. He now wishes to develop a forecast of the number of houses that will be sold by the agency over the next year. The agency€™s quarter-by-quarter sales figures over the last three years are shown below.(Use hand calculations below
The Andes Mining Company mines and ships copper ore. The company’s sales manager, Juanita Valdes, has been using the moving-average method based on the last three years of sales to forecast the demand for the next year. However, she has become dissatisfied with the inaccurate forecasts being
Reconsider Prob. 27.7-11. For each of the forecasting methods specified in parts (b), (c), and (d), use the corresponding procedure in the forecasting area of your IOR Tutorial to obtain the requested forecasts. After examining the accompanying graph that plots both the demand data and forecasts,
The Centerville Water Department provides water for the entire town and outlying areas. The number of acre-feet of water consumed in each of the four seasons of the three preceding years is shown below.(a) Determine the seasonal factors for the four seasons. (b) After considering seasonal effects,
Reconsider Prob. 27.5-3. Ralph Billett realizes that the last-value method is considered to be the naive forecasting method, so he wonders whether he should be using another method. Therefore, he has decided to use the available Excel templates that consider seasonal effects to apply various
Mark Lawrence€”the man with two first names€”has been pursuing a vision for more than two years. This pursuit began when he became frustrated in his role as director of human resources at Cutting Edge, a large company manufacturing computers and computer peripherals. At that
Long a market leader in the production of heavy machinery, the Spellman Corporation recently has been enjoying a steady increase in the sales of its new lathe. The sales over the past 10 months are shown below.Because of this steady increase, management has decided to use causal forecasting, with
Reconsider Probs. 27.7-3 and 27.6-1. Since the number of applications for admission submitted to Ivy College has been increasing at a steady rate, causal forecasting can be used to forecast the number of applications in future years by letting the year be the independent variable and the number of
Reconsider Prob. 27.7-11. Despite some fluctuations from year to year, note that there has been a basic trend upward in the annual demand for copper ore over the past 10 years. Therefore, by projecting this trend forward, causal forecasting can be used to forecast demands in future years by letting

Showing 36300 - 36400 of 88243

First
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
Last

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved