Introduction To Operations Research 7th Edition Frederick S. Hillier, Gerald J. Lieberman - Solutions

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A cargo plane has three compartments for storing cargo:front, center, and back. These compartments have capacity limits on both weight and space, as summarized below:
The Metalco Company desires to blend a new alloy of 40 percent tin, 35 percent zinc, and 25 percent lead from several available alloys having the following properties:The objective is to determine the proportions of these alloys that should be blended to produce the new alloy at a minimum cost.(a)
Al Ferris has $60,000 that he wishes to invest now in order to use the accumulation for purchasing a retirement annuity in 5 years. After consulting with his financial adviser, he has been offered four types of fixed-income investments, which we will label as investments A, B, C, D.Investments A
The Medequip Company produces precision medical diagnostic equipment at two factories. Three medical centers have placed orders for this month’s production output. The table below shows what the cost would be for shipping each unit from each factory to each of these customers. Also shown are the
Larry Edison is the director of the Computer Center for Buckly College. He now needs to schedule the staffing of the center. It is open from 8 A.M. until midnight. Larry has monitored the usage of the center at various times of the day, and determined that the following number of computer
Web Mercantile sells many household products through an online catalog. The company needs substantial warehouse space for storing its goods. Plans now are being made for leasing warehouse storage space over the next 5 months. Just how much space will be required in each of these months is known.
Ralph Edmund loves steaks and potatoes. Therefore, he has decided to go on a steady diet of only these two foods (plus some liquids and vitamin supplements) for all his meals. Ralph realizes that this isn’t the healthiest diet, so he wants to make sure that he eats the right quantities of the two
Consider the following model:subject to and(a) Use the graphical method to solve this model.(b) How does the optimal solution change if the objective function is changed to Z 40x1 70x2? (You may find it helpful to use the Graphical Analysis and Sensitivity Analysis procedure in IOR Tutorial.)(c)
Consider the following problem, where the value of c1 has not yet been ascertained.subject to and Use graphical analysis to determine the optimal solution(s) for(x1, x2) for the various possible values of c1.D,I
Use the graphical method to solve this problem:subject to x1 2x2 12
Use the graphical method to solve this problem:subject to and D,I
For each of the four assumptions of linear programming discussed in Sec. 3.3, write a one-paragraph analysis of how well it applies to each of the following examples given in Sec. 3.4.(a) Reclaiming solid wastes (Save-It Co.).(b) Personnel scheduling (Union Airways).(c) Distributing goods through a
For each of the four assumptions of linear programming discussed in Sec. 3.3, write a one-paragraph analysis of how well you feel it applies to each of the following examples given in Sec. 3.4:(a) Design of radiation therapy (Mary).(b) Regional planning (Southern Confederation of Kibbutzim).(c)
Read the referenced article that fully describes the OR study summarized in the second application vignette presented in Sec. 3.4.Briefly describe how linear programming was applied in this study.Then list the various financial and nonfinancial benefits that resulted from this study.
Read the referenced article that fully describes the OR study summarized in the first application vignette presented in Sec. 3.4.Briefly describe how linear programming was applied in this study.Then list the various financial and nonfinancial benefits that resulted from this study.
Consider a problem with two decision variables, x1 and x2, which represent the levels of activities 1 and 2, respectively. For each variable, the permissible values are 0, 1, and 2, where the feasible combinations of these values for the two variables are determined from a variety of constraints.
Reconsider Prob. 3.2-3, Indicate why each of the four assumptions of linear programming (Sec. 3.3) appears to be reasonably satisfied for this problem. Is one assumption more doubtful than the others? If so, what should be done to take this into account?
Suppose that the following constraints have been provided for a linear programming model.(a) Demonstrate that the feasible region is unbounded.(b) If the objective is to maximize Z x1 x2, does the model have an optimal solution? If so, find it. If not, explain why not.(c) Repeat part (b) when the
Use the graphical method to demonstrate that the following model has no feasible solutions.
Use the graphical method to find all optimal solutions for the following model:
This is your lucky day. You have just won a $10,000 prize. You are setting aside $4,000 for taxes and partying expenses, but you have decided to invest the other $6,000. Upon hearing this news, two different friends have offered you an opportunity to become a partner in two different
The shaded area in the following graph represents the feasible region of a linear programming problem whose objective function is to be maximized.Label each of the following statements as True or False, and then justify your answer based on the graphical method. In each case, give an example of an
The following table summarizes the key facts about two products, A and B, and the resources, Q, R, and S, required to produce them.
Consider the following problem, where the values of c1 and c2 have not yet been ascertained.
Consider the following problem, where the value of k has not yet been ascertained.Maximize Z x1 2x2 ,The solution currently being used is x1 2, x2 3. Use graphical analysis to determine the values of k such that this solution actually is optimal.
Consider the following problem, where the value of c1 has not yet been ascertained.subject to and Use graphical analysis to determine the optimal solution(s) for(x1, x2) for the various possible values of c1( c1 ).
The Omega Manufacturing Company has discontinued the production of a certain unprofitable product line. This accreated considerable excess production capacity. Management is considering devoting this excess capacity to one or more of three products; call them products 1, 2, and 3. The available
Weenies and Buns is a food processing plant which manufactures hot dogs and hot dog buns. They grind their own flour for the hot dog buns at a maximum rate of 200 pounds per week. Each hot dog bun requires 0.1 pound of flour. They currently have a contract with Pigland, Inc., which specifies that a
The Primo Insurance Company is introducing two new product lines: special risk insurance and mortgages. The expected profit is $5 per unit on special risk insurance and $2 per unit on mortgages.Management wishes to establish sales quotas for the new product lines to maximize total expected profit.
The WorldLight Company produces two light fixture(products 1 and 2) that require both metal frame parts and electric components. Management wants to determine how many units of each product to produce so as to maximize profit. For each unit of product 1, 1 unit of frame parts and 2 units of
The Whitt Window Company is a company with only threemployees which makes two different kinds of hand-crafted windows: a wood-framed and an aluminum-framed window. They ear$180 profit for each wood-framed window and $90 profit for eacaluminum-framed window. Doug makes the wood frames, and camake 6
Use the graphical method to solve the problem:subject to x2 10
Consider the following equation of a line:(a) Find the slope-intercept form of this equation.(b) Use this form to identify the slope and the intercept with the x2 axis for this line.(c) Use the information from part (b) to draw a graph of this line.D,I
Consider the following objective function for a linear programming model:(a) Draw a graph that shows the corresponding objective function lines for Z 6, Z 12, and Z 18.(b) Find the slope-intercept form of the equation for each of these three objective function lines. Compare the slope for these
For each of the following constraints, draw a separate graph to show the nonnegative solutions that satisfy this constraint.(a) x1 3x2 6(b) 4x1 3x2 12(c) 4x1 x2 8(d) Now combine these constraints into a single graph to show the feasible region for the entire set of functional
Read the referenced article that fully describes the OR study summarized in the application vignette presented in Sec. 3.1.Briefly describe how linear programming was applied in this study.Then list the various financial and nonfinancial benefits that resulted from this study
Read Selected Reference 4. The author describes 13 detailed phases of any OR study that develops and applies a computerbased model, whereas this chapter describes six broader phases.For each of these broader phases, list the detailed phases that fall partially or primarily within the broader phase.
From the bottom part of the selected references given at the end of the chapter, select three of these award-winning applications of the OR modeling approach (excluding any that have been assigned for other problems). For each one, read this article and write a one-page summary of the application
From the bottom part of the selected references given at the end of the chapter, select one of these award-winning applications of the OR modeling approach (excluding any that have been assigned for other problems). Read this article and then write a two-page summary of the application and the
Read Selected Reference A5 that describes an OR study done for IBM and the resulting computer system Optimizer.(a) Summarize the background that led to undertaking this study.(b) List the complicating factors that the OR team members faced when they started developing a model and a solution
Refer to pp. 163–167 of Selected Reference A4 that describes an OR study done for Yellow Freight System, Inc., and the resulting computer system SYSNET.(a) Briefly describe how the OR team gained the support of upper management for implementing SYSNET.(b) Briefly describe the implementation
Refer to Selected Reference A4 that describes an OR study done for Yellow Freight System, Inc.(a) Referring to pp. 147–149 of this article, summarize the background that led to undertaking this study.(b) Referring to p. 150, briefly describe the computer system SYSNET that was developed as a
Read Selected Reference A6 that describes an OR study done for Texaco.(a) Summarize the background that led to undertaking this study.(b) Briefly describe the user interface with the decision support system OMEGA that was developed as a result of this study.(c) OMEGA is constantly being updated and
Read pp. 603–617 of Selected Reference 3.(a) What does the author say about whether a model can be completely validated?(b) Summarize the distinctions made between model validity, data validity, logical/mathematical validity, predictive validity, operational validity, and dynamic validity.(c)
Read Selected Reference 7. Summarize the author’s viewpoint about the roles of observation and experimentation in the model validation process.
Refer to pp. 18–20 of Selected Reference A7 that describes an OR study done for the Rijkswaterstaat of the Netherlands. Describe an important lesson that was gained from model validation in this study.
Refer to Selected Reference 5.(a) Describe the author’s viewpoint about whether the sole goal in using a model should be to find its optimal solution.(b) Summarize the author’s viewpoint about the complementary roles of modeling, evaluating information from the model, and then applying the
Read Selected Reference A10 that describes an OR study done for Philips Electronics.(a) Summarize the background that led to undertaking this study.(b) What was the purpose of this study?(c) What were the benefits of developing software to support problem solving speedily?(d) List the four steps in
Read Selected Reference 5.(a) Identify the author’s example of a model in the natural sciences and of a model in OR.(b) Describe the author’s viewpoint about how basic precepts of using models to do research in the natural sciences can also be used to guide research on operations (OR).
Read Selected Reference A7 that describes an OR study done for the Rijkswaterstaat of the Netherlands. (Focus especially on pp. 3–20 and 30–32.)(a) Summarize the background that led to undertaking this study.(b) Summarize the purpose of each of the five mathematical models described on pp.
Read Selected Reference A3 that describes an OR study done for Swift & Company.(a) Summarize the background that led to undertaking this study.(b) Describe the purpose of each of the three general types of models formulated during this study.(c) How many specific models does the company now use as
Read the referenced article that fully describes the OR study summarized in the application vignette presented in Sec. 2.2. List the various financial and nonfinancial benefits that resulted from this study.
Read Selected Reference A9 that describes an OR study done for the Health Department of New Haven, Connecticut.(a) Summarize the background that led to undertaking this study.(b) Outline the system developed to track and test each needle and syringe in order to gather the needed data.(c) Summarize
Read Selected Reference A12 that describes an OR study done for the San Francisco Police Department.(a) Summarize the background that led to undertaking this study.(b) Define part of the problem being addressed by identifying the six directives for the scheduling system to be developed.(c) Describe
Read Selected Reference A1 that describes an awardwinning OR study done for General Motors.(a) Summarize the background that led to undertaking this study.(b) What was the goal of this study?(c) Describe how software was used to automate the collection of the needed data.(d) The improved production
The example in Sec. 2.1 summarizes an award-winning OR study done for Merrill Lynch. Read Selected Reference A2 that describes this study in detail.(a) Summarize the background that led to undertaking this study.(b) Quote the one-sentence statement of the general mission of the OR group (called the
Read the referenced article that fully describes the OR study summarized in the application vignette presented in Sec. 1.3. List the various financial and nonfinancial benefits that resulted from this study.
Select three of the applications of operations research listed in Table 1.1. For each one, read the article that is referenced in the application vignette presented in the section shown in the third column. (A link to all these articles is provided on our website, www.mhhe.com/hillier.) For each
Select one of the applications of operations research listed in Table 1.1. Read the article that is referenced in the application vignette presented in the section shown in the third column. (A link to all these articles is provided on our website, www.mhhe.com/hillier.) Write a two-page summary of
Select three of the applications of decision analysis listed in Table 15.5. Read the articles describing the applications in the indicated issues of Interfaces. For each one, write a one-page summary of the application and the benefits it provided.
Select one of the applications of decision analysis listed in Table 15.5. Read the article describing the application in the indicated issue of Interfaces. Write a two-page summary of the application and the benefits it provided.
You want to choose between actions A1 and A2 in the following decision tree, but you are uncertain about the value of the probability p, so you need to perform sensitivity analysis of p as well.Your utility function for money (the payoff received) is u(M) (a) For p 0.25, determine which action is
Consider the following decision tree, where the probabilities for each chance fork are shown in parentheses.The dollar amount given next to each branch is the cash flow generated along that branch, where these intermediate cash flows add up to the total net cash flow shown to the right of each
Dr. Switzer has a seriously ill patient but has had trouble diagnosing the specific cause of the illness. The doctor now has narrowed the cause down to two alternatives: disease A or disease B. Based on the evidence so far, she feels that the two alternatives are equally likely.Beyond the testing
Use TreePlan to construct and solve the resulting decision tree in turn for p 0.25, p 0.5, and p 0.75.
You are given the following payoff table:(a) Assume that your utility function for the payoffs is u(x) x.Plot the expected utility of each alternative action versus the value of p on the same graph. For each alternative action, find the range of values of p over which this alternative maximizes
You wish to construct your personal utility function u(M)for receiving M thousand dollars. After setting u(0) 0, you next set u(1) 1 as your utility for receiving $1,000. You next want to find u(10) and then u(5).(a) You offer yourself the following two hypothetical alternatives:A1: Obtain $10,000
Which choice should you make to maximize expected utility?
For your graduation present from college, your parents are offering you your choice of two alternatives The first alternative is to give you a money gift of $19,000. The second alternative is to make an investment in your name. This investment will quickly have the following two possible
You live in an area that has a possibility of incurring a massive earthquake, so you are considering buying earthquake insurance on your home at an annual cost of $180. The probability of an earthquake damaging your home during 1 year is 0.001. If this happens, you estimate that the cost of the
Reconsider the Goferbroke Co. prototype example, including the application of utilities in Sec. 15.5. The owner now has decided that, given the company’s precarious financial situation, he needs to take a much more risk-averse approach to the problem. Therefore, he has revised the utilities given
The executive search being conducted for Western Bank by Headhunters Inc. may finally be bearing fruit. The position to be filled is a key one—Vice President for Information Processing—because this person will have responsibility for developing a state-of-the-art management information system
Chelsea Bush is an emerging candidate for her party’s nomination for President of the United States. She now is considering whether to run in the high-stakes Super Tuesday primaries.If she enters the Super Tuesday (S.T.) primaries, she and her advisers believe that she will either do well (finish
Use the scenario given in Prob. 15.3-13.(a) Draw and properly label the decision tree. Include all the payoffs but not the probabilities.T (b) Find the probabilities for the branches emanating from the chance forks.(c) Apply the backward induction procedure, and identify the resulting optimal
Use the scenario given in Prob. 15.3-12.(a) Draw and properly label the decision tree. Include all the payoffs but not the probabilities.T (b) Find the probabilities for the branches emanating from the chance forks.(c) Apply the backward induction procedure, and identify the resulting optimal
Use the scenario given in Prob. 15.3.-11.(a) Draw and properly label the decision tree. Include all the payoffs but not the probabilities.T (b) Find the probabilities for the branches emanating from the chance forks.(c) Apply the backward induction procedure, and identify the resulting optimal
The Morton Ward Company is considering the introduction of a new product that is believed to have a 50-50 chance of being successful. One option is to try out the product in a test market, at a cost of $5 million, before making the introduction decision. Past experience shows that ultimately
Use the scenario given in Prob. 15.3-9.(a) Draw and properly label the decision tree. Include all the payoffs but not the probabilities.T (b) Find the probabilities for the branches emanating from the chance forks.(c) Apply the backward induction procedure, and identify the resulting optimal policy.
Jose Morales manages a large outdoor fruit stand in one of the less affluent neighborhoods of San Jose, California. To replenish his supply, Jose buys boxes of fruit early each morning from a grower south of San Jose. About 90 percent of the boxes of fruit turn out to be of satisfactory quality,
Use the scenario given in Prob. 15.3-7.(a) Draw and properly label the decision tree. Include all the payoffs but not the probabilities.T (b) Find the probabilities for the branches emanating from the chance forks.(c) Apply the backward induction procedure, and identify the resulting optimal policy.
On Monday, a certain stock closed at $10 per share. On Tuesday, you expect the stock to close at $9, $10, or $11 per share, with respective probabilities 0.3, 0.3, and 0.4. On Wednesday, you expect the stock to close 10 percent lower, unchanged, or 10 percent higher than Tuesday’s close, with the
The comptroller of the Macrosoft Corporation has $100 million of excess funds to invest. She has been instructed to invest the entire amount for 1 year in either stocks or bonds (but not both)and then to reinvest the entire fund in either stocks or bonds (but not both) for 1 year more. The
The Athletic Department of Leland University is considering whether to hold an extensive campaign next year to raise funds for a new athletic field. The response to the campaign depends heavily upon the success of the football team this fall. In the past, the football team has had winning seasons
You are given the decision tree below, with the probabilities at chance forks shown in parentheses and with the payoffs at terminal points shown on the right. Analyze this decision tree to obtain the optimal policy.
You are given the decision tree to the right, where the numbers in parentheses are probabilities and the numbers on the far right are payoffs at these terminal points.(a) Analyze this decision tree to obtain the optimal policy.A (b) Use TreePlan to construct and solve the same decision tree.
The management of Silicon Dynamics now wants to see a decision tree displaying the entire problem.(a) Construct and solve this decision tree by hand.A (b) Use TreePlan to construct and solve this decision tree.
There are two biased coins with probabilities of landing heads of 0.8 and 0.4, respectively. One coin is chosen at random(each with probability 1 2) to be tossed twice. You are to receive $100 if you correctly predict how many heads will occur in two tosses.T (a) Using Bayes’ decision rule,
Sell the film for $1.(a) If the six states of nature correspond to 0, 1, 2, 3, 4, and 5 defective sheets in the package, complete the following payoff table:These data indicate that each state of nature is equally likely, so that this prior distribution can be assumed. What is the optimal action
Sell the film for $2.
Scrap the film.
A new type of photographic film has been developed. It is packaged in sets of five sheets, where each sheet provides an instantaneous snapshot. Because this process is new, the manufacturer has attached an additional sheet to the package, so that the store may test one sheet before it sells the
Consider two weighted coins. Coin 1 has a probability of 0.3 of turning up heads, and coin 2 has a probability of 0.6 of turning up heads. A coin is tossed once; the probability that coin 1 is tossed is 0.6, and the probability that coin 2 is tossed is 0.4.The decision maker uses Bayes’ decision
Past experience indicates that p for an entire lot is either 0.05 or 0.25. Furthermore, in 80 percent of the lots produced, p equals 0.05 (so p equals 0.25 in 20 percent of the lots).These items are then used in an assembly, and ultimately their quality is determined before the final assembly
The Hit-and-Miss Manufacturing Company produces items that have a probability p of being defective. These items are produced in lots of
Management of the Telemore Company is considering developing and marketing a new product. It is estimated to be twice as likely that the product would prove to be successful as unsuccessful. It it were successful, the expected profit would be$1,500,000. If unsuccessful, the expected loss would
An athletic league does drug testing of its athletes, 10 percent of whom use drugs. This test, however, is only 95 percent reliable. That is, a drug user will test positive with probability 0.95 and negative with probability 0.05, and a nonuser will test negative with probability 0.95 and positive
Vincent Cuomo is the credit manager for the Fine Fabrics Mill. He is currently faced with the question of whether to extend $100,000 credit to a potential new customer, a dress manufacturer. Vincent has three categories for the credit-worthiness of a company: poor risk, average risk, and good risk,
Find the optimal action under Bayes’ decision rule.
Suppose now that the Air Force knows that a similar type of engine was produced for an earlier version of the type of airplane currently under consideration.The order size for this earlier version was the same as for the current type. Furthermore, the probability distribution of the number of spare
You are given the opportunity to guess whether a coin is fair or two-headed, where the prior probabilities are 0.5 for each of these possibilities. If you are correct, you win $5; otherwise, you lose $5. You are also given the option of seeing a demonstration flip of the coin before making your

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Introduction To Operations Research 7th Edition Frederick S. Hillier, Gerald J. Lieberman - Solutions

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