- The game of blackjack (sometimes called “21”) is a popular casino game. The goal is to have a hand with a value of 21 or as close to 21 as possible without exceeding 21. The player and the dealer
- Rock-Paper-Scissors is a simple game in which two players compete by simultaneously choosing rock, paper, or scissors. According to the classic rules of the game, paper beats rock, scissors beats
- One cause of the downtime in Problem 3 was traced to a specific piece of computer hardware. Management believes that switching to a different hardware component will result in the following
- County Beverage Drive-Thru, Inc., operates a chain of beverage supply stores in northern Illinois. Each store has a single service lane; cars enter at one end of the store and exit at the other end.
- Harbor Dunes Golf Course was recently honored as one of the top public golf courses in South Carolina. The course, situated on land that was once a rice plantation, offers some of the best views of
- What will your portfolio be worth in 10 years? In 20 years? When you stop working? The Human Resources Department at Tri-State Corporation was asked to develop a financial planning model that would
- Develop your own worksheet for the Butler inventory simulation model shown in Figure 16.10. Suppose that management prefers not to charge for loss of goodwill. Run the Butler inventory simulation
- Develop your own worksheet for the Butler inventory simulation model shown in Figure 16.10. Suppose that management prefers not to charge for loss of goodwill. Run the Butler inventory simulation
- Develop your own worksheet for the PortaCom simulation model described in Section 16.1. a. Compute the mean profit, the minimum profit, and the maximum profit. b. What is your estimate of
- Over a five-year period, the quarterly change in the price per share of common stock for a major oil company ranged from -8% to 12%. A financial analyst wants to learn what can be expected for price
- Office Equipment, Inc. (OEI) leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair
- Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 A.M. to 11:00 A.M. time period, calls to the reservation agent occur randomly at an average
- A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per
- The River City Fire Department (RCFD) fights fires and provides a variety of rescue operations in the River City metropolitan area. The RCFD staffs 13 ladder companies, 26 pumper companies, and
- Managers at Wagner Fabricating Company are reviewing the economic feasibility of manufacturing a part that the company currently purchases from a supplier. Forecasted annual demand for the part is
- The port of Lajitas has three loading docks. The distance (in meters) among the loading docks is given in the following table:Three tankers currently at sea are coming into Lajitas. It is necessary
- Using the return data in Table 12.17, construct a portfolio from Apple, AMD, and Oracle that matches the Information Technology S&P index as closely as possible. Use the return data for the
- Formulate and solve the Markowitz portfolio optimization model that was introduced in Problem 18 using the return data in columns five, six, and seven of Figure 12.17. In this case, nine scenarios
- Formulate and solve the Markowitz portfolio optimization model that was introduced in Problem 18 using the return data in columns five, six, and seven of Figure 12.17. In this case, nine scenarios
- Harry Markowitz received the 1990 Nobel Prize for his path-breaking work in portfolio optimization. One version of the Markowitz model is based on minimizing the variance of the portfolio subject to
- Harry Markowitz received the 1990 Nobel Prize for his path-breaking work in portfolio optimization. One version of the Markowitz model is based on minimizing the variance of the portfolio subject to
- Harry Markowitz received the 1990 Nobel Prize for his path-breaking work in portfolio optimization. One version of the Markowitz model is based on minimizing the variance of the portfolio subject to
- Reconsider the Leisure Airlines problem from Section 12.2. Suppose that as of May 1 the following number of seats have been sold: a. Determine how many seats are still available for sale on
- In Section 12.1 data envelopment analysis was used to evaluate the relative efficiencies of four hospitals. Data for three input measures and four output measures were provided in Tables 12.1 and
- Buckeye Manufacturing produces heads for engines used in the manufacture of trucks. The production line is highly complex, and it measures 900 feet in length. Two types of engine heads are produced
- Using aggressive mail promotion with low introductory interest rates, Yeager National Bank (YNB) built a large base of credit card customers throughout the continental United States. Currently, all
- The Darby Company manufactures and distributes meters used to measure electric power consumption. The company started with a small production plant in El Paso and gradually built a customer base
- Solutions Plus is an industrial chemicals company that produces specialized cleaning fluids and solvents for a wide variety of applications. Solutions Plus just received an invitation to submit a bid
- Cleveland Area Rapid Delivery (CARD) operates a delivery service in the Cleveland metropolitan area. Most of CARD’s business involves rapid delivery of documents and parcels between offices during
- Duke Energy manufactures and distributes electricity to customers in the United States and Latin America. Duke Energy acquired Cinergy Corporation in 2005, which had generating facilities and energy
- Davis Instruments has two manufacturing plants located in Atlanta, Georgia. Product demand varies considerably from month to month, causing Davis extreme difficulty in workforce scheduling. Recently
- The Scottsville Textile Mill produces five different fabrics. Each fabric can be woven on one or more of the mill’s 38 looms. The sales department’s forecast of demand for the next month is shown
- Phoenix Computer manufactures and sells personal computers directly to customers. Orders are accepted by phone and through the company’s website. Phoenix will be introducing several new laptop
- The Flamingo Grill is an upscale restaurant located in St. Petersburg, Florida. To help plan an advertising campaign for the coming season, Flamingo’s management team hired the advertising firm of
- Morton Financial must decide on the percentage of available funds to commit to each of two investments, referred to as A and B, over the next four periods. The following table shows the amount of new
- The Ferguson Paper Company produces rolls of paper for use in cash registers. The rolls, which are 200 feet long, are produced in widths of 11⁄2, 21⁄2, and 31⁄2 inches. The production process
- The production manager for the Classic Boat Corporation must determine how many units of the Classic 21 model to produce over the next four quarters. The company has a beginning inventory of 100
- As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the following annual payments (in thousands of dollars): The annual
- Gulf Coast Electronics is ready to award contracts for printing its annual report. For the past several years, the four-color annual report has been printed by Johnson Printing and Lakeside Litho. A
- The program manager for Channel 10 would like to determine the best way to allocate the time for the 11:00–11:30 evening news broadcast. Specifically, she would like to determine the number of
- Cranberries can be harvested using either a “wet” method or a “dry” method. Dry-harvested cranberries can be sold at a premium, while wet-harvested cranberries are used mainly for cranberry
- Davison Electronics manufactures two LCD television monitors, identified as model A andmodel B. Each model has its lowest possible production cost when produced on Davison’s new production line.
- The Porsche Club of America sponsors driver education events that provide highperformance driving instruction on actual racetracks. Because safety is a primary consideration at such events, many
- Tucker Inc. produces high-quality suits and sport coats for men. Each suit requires 1.2 hours of cutting time and 0.7 hours of sewing time, uses 6 yards of material, and provides a profit
- Digital Controls, Inc. (DCI) manufactures two models of a radar gun used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus 1 mile per hour, whereas the smaller
- Refer to the sensitivity report in Figure 8.18. a. Identify the range of optimality for each objective function coefficient. b. Suppose the profit for the economy model is increased by $6
- Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respectively. The production
- Refer to Problem 10 and the sensitivity report shown in Figure 8.17. a. Suppose the risk index for the stock fund (the objective function coefficient for S) increases from its current value of
- Recall the Innis Investments problem (Chapter 7, Problem 39). Letting S = units purchased in the stock fund M = units purchased in the money market fundleads to
- Recall the Tom’s, Inc., problem (Chapter 7, Problem 28). Letting W = jars of Western Foods Salsa M = jars of Mexico City Salsaleads
- Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of U.S. Oil and H shares of Huber Steel. The
- Refer to the Kelson Sporting Equipment problem (Chapter 7, Problem 24). Letting R = number of regular gloves C =
- Consider the linear program in Problem 1. The value of the optimal solution is 27. Suppose that the right-hand side for constraint 1 is increased from 10 to 11. a. Use the graphical solution
- Hart Venture Capital (HVC) specializes in providing venture capital for software development and Internet applications. Currently HVC has two investment opportunities: (1) Security Systems, a firm
- Better Fitness, Inc. (BFI) manufactures exercise equipment at its plant in Freeport, Long Island. It recently designed two universal weight machines for the home exercise market. Both machines use
- South Shore Construction builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from
- Air pollution control specialists in southern California monitor the amount of ozone, carbon dioxide, and nitrogen dioxide in the air on an hourly basis. The hourly time series data exhibit
- The following table reports the percentage of stocks in a portfolio for nine quarters from 2007 to 2009. Quarter
- Refer again to the gasoline sales time series data in Table 6.1. a. Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for third most recent, compute
- ABC Inc. and XYZ Co. are the two dominant companies providing chargers, adapters, and other accessories for cell phones. Each of these Silicon Valley companies is developing a new line of smartphone
- A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons (Statesman, January 28, 2008). The survey found that 23% of the respondents have boycotted
- It is commonly asserted that the Durbin–Watson statistic is only appropriate for testing for first-order autoregressive disturbances. What combination of the coefficients of the model is estimated
- The following regression is obtained by ordinary least squares, using 21 observations. (Estimated asymptotic standard errors are shown in parentheses.)yt = 1.3 + 0.97yt−1 + 2.31xt, D −W =
- Derive the disturbance covariance matrix for the modelyt = βxt + εt,εt = ρεt−1 + ut − λut−1.What parameter is estimated by the regression of the OLS residuals on their lagged values?
- Does first differencing reduce autocorrelation? Consider the models yt = β'xt + εt, where εt = ρεt−1 + ut and εt = ut −λut−1. Compare the autocorrelation of εt in the original model
- Prove that the Hessian for the tobit model in (19-14) is negative definite after Olsen’s transformation is applied to the parameters.
- Derive the partial effects for the tobit model with heteroscedasticity that is described in Section 19.3.5.a.
- Continuing to use the data in Exercise 1, consider once again only the nonzero observations. Suppose that the sampling mechanism is as follows: y∗ and another normally distributed random variable z
- Using only the nonlimit observations, repeat Exercise 2 in the context of the truncated regression model. Estimate μ and σ by using the method of moments estimator outlined in Example 19.2. Compare
- We now consider the tobit model that applies to the full data set.a. Formulate the log-likelihood for this very simple tobit model.b. Reformulate the log-likelihood in terms of θ = 1/σ and γ =
- Consider estimation of a Poisson regression model for yi |xi. The data are truncated on the left—these are on-site observations at a recreasion site, so zeros do not appear in the data set. The
- For the zero-inflated Poisson (ZIP) model in Section 18.4.8, we derived the conditional mean function, E[yi |xi, wi] = (1 − Fi)λi.a. For the same model, now obtain Var[yi |xi, wi]. Then, obtain
- We are interested in the ordered probit model. Our data consist of 250 observations, of which the responses are Using the preceding data, obtain maximum likelihood estimates of the unknown
- In the panel data models estimated in Section 17.4, neither the logit nor the probit model provides a framework for applying a Hausman test to determine whether fixed or random effects is preferred.
- Prove (17-29). In Lo = n[Pln P + (1 – P) In(1 – P)], %3D
- A data set consists of n = n1 + n2 + n3 observations on y and x. For the first n1 observations, y = 1 and x = 1. For the next n2 observations, y = 0 and x = 1. For the last n3 observations, y = 0 and
- The following hypothetical data give the participation rates in a particular type of recycling program and the number of trucks purchased for collection by 10 towns in a small mid-Atlantic
- Construct the Lagrange multiplier statistic for testing the hypothesis that all the slopes (but not the constant term) equal zero in the binomial logit model. Prove that the Lagrange multiplier
- Given the data set estimate a probit model and test the hypothesis that x is not influential in determining the probability that y equals one. 1 0 0 1 1 0 0 1 1 9 2 5 4 6 7 3 5 2 6' 1
- Suppose that a linear probability model is to be fit to a set of observations on a dependent variable y that takes values zero and one, and a single regressor x that varies continuously across
- Abinomial probability model is to be based on the following index function model: y?? = α + βd + ε, y = 1, if y?? > 0, y = 0 otherwise. The only regressor, d, is a dummy variable. The data
- Suppose the distribution of yi| λ is Poisson, We will obtain a sample of observations, yi , . . . , yn. Suppose our prior for λ is the inverted gamma, which will imply a. Construct the
- Prove the result claimed in Example 4.7. Greene (1980a) considers estimation in a regression model with an asymmetrically distributed disturbance, where ε has the gamma distribution in Section
- Consider sampling from a multivariate normal distribution with mean vector μ = (μ1, μ2, . . . , μM) and covariance matrix σ2I. The log-likelihood function is Show that the maximum likelihood
- For random sampling from the classical regression model in (14-3), reparameterize the likelihood function in terms of η = 1/σ and δ = (1/σ)β. Find the maximum likelihood estimators of η and δ
- Show that the likelihood inequality in Theorem 14.3 holds for the normal distribution. Eo[(1/n) In L(@%)] > Eo[(1/n) In L(0)] for any e + 00 (including ô).
- Show that the likelihood inequality in Theorem 14.3 holds for the Poisson distribution used in Section 14.3 by showing that E[(1/n) ln L(θ | y)] is uniquely maximized at θ = θ0.
- Consider a bivariate distribution for x and y that is a function of two parameters, α and β. The joint density is f (x, y | α, β). We consider maximum likelihood estimation of the two parameters.
- The following data were generated by the Weibull distribution of Exercise 4: a. Obtain the maximum likelihood estimates of α and β, and estimate the asymptotic covariance matrix for the
- Suppose that x has theWeibull distribution a. Obtain the log-likelihood function for a random sample of n observations. b. Obtain the likelihood equations for maximum likelihood estimation of α
- Mixture distribution. Suppose that the joint distribution of the two random variables x and y is a. Find the maximum likelihood estimators of β and θ and their asymptotic joint distribution. b.
- The following table presents a hypothetical panel of data: a. Estimate the groupwise heteroscedastic model of Section 9.7.2. Include an estimate of the asymptotic variance of the slope estimator.
- Suppose that in the groupwise heteroscedasticity model of Section 9.7.2, Xi is the same for all i.What is the generalized least squares estimator of β? How would you compute the estimator if it were
- The model satisfies the groupwise heteroscedastic regression model of Section 9.7.2 All variables have zero means. The following sample second-moment matrix is obtained from a sample of 20
- Two-way random effects model. We modify the random effects model by the addition of a time-specific disturbance. Thus, where Write out the full disturbance covariance matrix for a data set with n
- A two-way fixed effects model. Suppose that the fixed effects model is modified to include a time-specific dummy variable as well as an individual-specific variable. Then yit= αi+ γt + xitβ +
- What are the probability limits of (1/n)LM, where LM is defined in (11-42) under the null hypothesis that σ2u = 0 and under the alternative that σ2u ≠ 0?
- Unbalanced design for random effects. Suppose that the random effects model of Section 11.5 is to be estimated with a panel in which the groups have different numbers of observations. Let Ti be the
- Suppose that the fixed effects model is formulated with an overall constant term and n− 1 dummy variables (dropping, say, the last one). Investigate the effect that this supposition has on the set
- The following is a panel of data on investment (y) and profit (x) for n = 3 firms over T = 10 periods. a. Pool the data and compute the least squares regression coefficients of the model yit = α +