Questions and Answers of Introduction To Operations Research

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
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
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
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,
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
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
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)
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
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
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
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
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
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
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
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 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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
You are given the following payoff table (in units of dollars):You have the option of paying $100 to have research done to better predict which state of nature will occur. When the true state of
Reconsider the Goferbroke Co. prototype example, including its analysis in Sec. 15.3. With the help of a consulting geologist, some historical data have been obtained that provide more precise
Using Bayes’ decision rule, consider the decision analysis problem having the following payoff table (in units of thousands of dollars):.T (a) Which alternative should be chosen? What is the
Betsy Pitzer makes decisions according to Bayes’ decision rule. For her current problem, Betsy has constructed the following payoff table (in units of dollars):T (a) Which alternative should Betsy
You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem:T (a) According to Bayes’ decision rule, which alternative should be chosen?T (b) Find
Management of Silicon Dynamics now is considering doing full-fledged market research at a cost of $1 million to predict which of the two levels of demand is likely to occur. Previous experience
An individual makes decisions according to Bayes’ decision rule. For her current problem, she has constructed the following payoff table, and she now wishes to maximize the expected payoff.The
The cost of a spare engine purchased now is $400,000, whereas the cost of a spare engine purchased at a later date is $900,000.Spares must always be supplied if they are demanded, and unused engines
A new type of airplane is to be purchased by the Air Force, and the number of spare engines to be ordered must be determined. The Air Force must order these spare engines in batches of five, and it
Dwight Moody is the manager of a large farm with 1,000 acres of arable land. For greater efficiency, Dwight always devotes the farm to growing one crop at a time. He now needs to make a decision on
You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem:T (a) Which alternative should be chosen under the maximin payoff criterion?T (b) Which
Consider a decision analysis problem whose payoffs (in units of thousands of dollars) are given by the following payoff table:T (a) Which alternative should be chosen under the maximin payoff
Warren Buffy decides that Bayes’decision rule is his most reliable decision criterion. He believes that 0.1 is just about right as the prior probability of an improving economy, but is quite
Reconsider Prob.
Warren Buffy is an enormously wealthy investor who has built his fortune through his legendary investing acumen. He currently has been offered three major investments and he would like to choose one.
Jean Clark is the manager of the Midtown Saveway Grocery Store. She now needs to replenish her supply of strawberries.Her regular supplier can provide as many cases as she wants. However, because
Silicon Dynamics has developed a new computer chip that will enable it to begin producing and marketing a personal computer if it so desires. Alternatively, it can sell the rights to the computer
Which action (drill for oil or sell the land) should be chosen?
Should a seismic survey be conducted before an action is chosen?
An oil company deciding whether to drill for oil in a particular location. How likely is oil there? How much? How deep will they need to drill? Should geologists investigate the site further before
An agricultural firm selecting the mix of crops and livestock for the upcoming season.What will be the weather conditions? Where are prices headed? What will costs be?
A government contractor bidding on a new contract. What will be the actual costs of the project? Which other companies might be bidding? What are their likely bids?
A financial firm investing in securities. Which are the market sectors and individual securities with the best prospects? Where is the economy headed? How about interest rates? How should these
A manufacturer introducing a new product into the marketplace. What will be the reaction of potential customers? How much should be produced? Should the product be test marketed in a small region
Consider the following problem.Maximize Z 3x1 7x2 2x3, subject to2x1 2x2 x3 103x1 x2 x3 20 and x1 0, x2 0, x3 0.You are given the fact that the basic variables in the optimal
Consider the following problem.Maximize Z 2x1 4x2 3x3, subject to x1 3x2 2x3 20 x1 5x2 2x3 10 and x1 0, x2 0, x3 0.Let x4 be the artificial variable for the first constraint. Let
Consider the following problem.Minimize Z 2x1 3x2 2x3, subject to x1 4x2 2x3 8 3x1 2x2 2x3 6 and x1 0, x2 0, x3 0.Let x4 and x6 be the surplus variables for the first and second
Use artificial variables and the Big M method to construct the complete first sim-plex tableau for the simplex method, and then identify the columns that will contains S* for applying the fundamental
For iteration 2 of the example in Sec. 5.3, the following expression was shown:Final row 0 [3, 5 0, 0, 0 0] [0, 3 2, 1] .Derive this expression by combining the algebraic operations (in matrix
Consider the following problem.Maximize Z c1x1 c2x2 c3x3, subject to x1 2x2 x3 b 2x1 x2 3x3 2b and x1 0, x2 0, x3 0.Note that values have not been assigned to the coefficients in
You are using the simplex method to solve the following linear programming problem.Maximize Z 6x1 5x2 x3 4x4, subject to 3x1 2x2 3x3 x4 120 3x1 3x2 x3 3x4 180 and x1 0, x2 0, x3
Consider the following problem.Maximize Z 20x1 6x2 8x3, subject to 8x1 2x2 3x3 200 4x1 3x2 3x3 100 2x1 3x2 x3 50 2x1 3x2 x3 20 and x1 0, x2 0, x3 0.Let x4, x5, x6, and x7
Consider the following problem.Maximize Z x1 x2 2x3, subject to x1 x2 3x3 15 2x1 x2 x3 2x1 x2 x3 4 and x1 0, x2 0, x3 0.Let x4, x5, and x6 denote the slack variables for the
Consider the following problem.Maximize Z 6x1 x2 2x3, subject to2x1 2x2 1 2x3 24x1 2x2 3 2x3 32x1 2x2 1 2x3 1 and x1 0, x2 0, x3 0.Let x4, x5, and x6 denote the slack variables
Consider the following problem.Maximize Z 4x1 3x2 x3 2x4, subject to 4x1 2x2 x3 x4 5 3x1 x2 2x3 x4 4 and x1 0, x2 0, x3 0, x4 0.Let x5 and x6 denote the slack variables for
Work through the revised simplex method step by step to solve each of the following models:(a) Model given in Prob. 3.1-5.(b) Model given in Prob. 4.7-8.D 5.3-1.* Consider the following
Work through the revised simplex method step by step to solve the model given in Prob. 4.7-6.I
Work through the revised simplex method step by step to solve the model given in Prob. 4.1-5.I
For the sequence of CPF solutions identified in part (e), construct the basis matrix B for each of the corresponding BF solutions. For each one, invert B manually, use this B1 to calculate the
Reconsider Prob.
Consider the following problem.Maximize Z 8x1 4x2 6x3 3x4 9x5, subject to x1 2x2 3x3 3x4 x5 180 (resource 1)4x1 3x2 2x3 x4 x5 270 (resource 2)x1 3x2 2x3 x4 3x5 180
The formula for the line passing through (2, 4, 3) and(4, 2, 4) in Fig. 5.2 can be written as(2, 4, 3) [(4, 2, 4) (2, 4, 3)] (2, 4, 3) (2, 2, 1), where 0 1 for just the line segment between
Consider the three-variable linear programming problem shown in Fig. 5.2.(a) Construct a table like Table 5.4, giving the indicating variable for each constraint boundary equation and original
Consider the following problem.Maximize Z 3x1 4x2 2x3, subject to x1 x2 x3 20 x1 2x2 x3 30 and x1 0, x2 0, x3 0.Let x4 and x5 be the slack variables for the respective functional
Consider the following problem.Maximize Z 2x1 2x2 3x3, subject to 2x1 x2 2x3 4 x1 x2 x3 3 and x1 0, x2 0, x3 0.Let x4 and x5 be the slack variables for the respective functional
Consider the linear programming problem given in Table 6.1 as the dual problem for the Wyndor Glass Co. example.Coefficient of:Basic Right Iteration Variable Eq. Z x1 x2 x3 x4 x5 x6 Side Z (0) 1 0 1
Consider the following problem.Maximize Z 2x1 x2 x3, subject to 3x1 x2 x3 60 x1 x2 2x3 10 x1 x2 x3 20 and x1 0, x2 0, x3 0.After slack variables are introduced and then one
Consider the original form (before augmenting) of a linear programming problem with n decision variables (each with a nonnegativity constraint) and m functional constraints. Label each of the
Each of the following statements is true under most circumstances, but not always. In each case, indicate when the statement will not be true and why.(a) The best CPF solution is an optimal
Reconsider the model in Prob. 3.1-4.(a) Identify the 15 sets of defining equations for this problem. For each one, solve (if a solution exists) for the corresponding corner-point solution, and
Reconsider the model in Problem 4.6-3.(a) Identify the 10 sets of defining equations for this problem. For each one, solve (if a solution exists) for the corresponding corner-point solution, and
Consider the following problem.Minimize Z x1 2x2, subject tox1 x2 152x1 x2 902x1 x2 30 and x1 0, x2 0.(a) Solve this problem graphically.(b) Develop a table giving each of the CPF
Consider the linear programming problem given in Table 6.1 as the dual problem for the Wyndor Glass Co. example.(a) Identify the 10 sets of defining equations for this problem. For each one, solve
Consider the three-variable linear programming problem shown in Fig. 5.2.(a) Construct a table like Table 5.1, giving the set of defining equations for each CPF solution.(b) What are the defining
Consider the following problem.Maximize Z 2x1 x2 x3, subject to 3x1 x2 x3 60 x1 x2 2x3 10 x1 x2 x3 20 and x1 0, x2 0, x3 0.After slack variables are introduced and then one
Consider the following problem.Maximize Z 2x1 3x2, subject to3x1 x2 14x1 2x2 204x1 x2 10x1 2x2 5 and x1 0, x2 0.(a) Solve this problem graphically. Identify the CPF solutions by
Repeat Prob. 5.1-1 for the model in Prob. 3.1-5.
Consider the following problem.Maximize Z 3x1 2x2, subject to 2x1 x2 6 x1 2x2 6 and x1 0, x2 0.(a) Solve this problem graphically. Identify the CPF solutions by circling them on the
Consider the following problem.Maximize Z 2x1 x2 3x3, subject to x1 x2 x3 3 x1 2x2 x3 1 x1 2x2 x3 2 and x1 0, x2 0, x3 0.Suppose that the Big M method (see Sec. 4.6) is used

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