Steve Goodman, production foreman for the Florida Gold Fruit Company, estimates that the average sale of oranges is 4,700 and the standard deviation is 500 oranges. Sales follow a normal distribution. (a) What is the probability that sales will be greater than 5,500 oranges? (b) What is the probability that sales will be greater than 4,500 oranges? (c) What is the probability that sales will be less than 4,900 oranges? (d) What is the probability that sales will be less than 4,300 oranges?
> What is the SSE? How is this related to the SST and the SSR?
> What is the difference between prior and posterior probabilities?
> What information should be placed on a decision tree?
> What is the overall purpose of utility theory?
> What is the break-even point? What parameters are necessary to find it?
> C. W. Churchman once said that “mathematics … tends to lull the unsuspecting into believing that he who thinks elaborately thinks well.” Do you think that the best QA models are the ones that are most elaborate and complex mathematically? Why?
> How is the efficiency of sample information computed?
> What is the EVSI? How is this computed?
> Managers are quick to claim that quantitative analysts talk to them in a jargon that does not sound like English. List four terms that might not be understood by a manager. Then explain in nontechnical language what each term means.
> Describe how you would determine the best decision using the EMV criterion with a decision tree.
> What is a random variable? What are the various types of random variables?
> What is implementation, and why is it important?
> Describe the characteristics of a Bernoulli process. How is a Bernoulli process associated with the binomial distribution?
> Give some examples of various types of models. What is a mathematical model? Develop two examples of mathematical models.
> What techniques are used to solve decision-making problems under uncertainty? Which technique results in an optimistic decision? Which technique results in a pessimistic decision?
> Explain how a scatter diagram can be used to identify the type of regression to use.
> Describe the various approaches used in determining probability values.
> What is a time-series forecasting model?
> What is the meaning of least squares in a regression model?
> Beverly Mills has decided to lease a hybrid car to save on gasoline expenses and to do her part to help keep the environment clean. The car she selected is available from only one dealer in the local area, but that dealer has several leasing options to a
> Define opportunity loss. What decision-making criteria are used with an opportunity loss table?
> Even though independent gasoline stations have been having a difficult time, Susan Solomon has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual r
> Mick Karra is the manager of MCZ Drilling Products, which produces a variety of specialty valves for oil field equipment. Recent activity in the oil fields has caused demand to increase drastically, and a decision has been made to open a new manufacturin
> In Problem 3-27, Farm Grown, Inc., has reason to believe the probabilities may not be reliable due to changing conditions. If these probabilities are ignored, what decision would be made using the optimistic criterion? What decision would be made using t
> Farm Grown, Inc., produces cases of perishable food products. Each case contains an assortment of vegetables and other farm products. Each case costs $5 and sells for $15. If there are any cases not sold by the end of the day, they are sold to a large fo
> Brilliant Color is a small supplier of chemicals and equipment that are used by some photographic stores to process 35mm film. One product that Brilliant Color supplies is BC-6. John Kubick, president of Brilliant Color, normally stocks 11, 12, or 13 cas
> In Problem 3-22, you helped Allen Young determine the best investment strategy. Now, Allen is thinking about paying for a stock market newsletter. A friend of Allen said that these types of letters could predict very accurately whether the market would b
> Mickey Lawson is considering investing some money that he inherited. The following payoff table gives the profits that would be realized during the next year for each of three investment alternatives Mickey is considering: (a) What decision would maxim
> In the Arnold’s Muffler example for the exponential distribution in this chapter, the average rate of service was given as 3 per hour, and the times were expressed in hours. Convert the average service rate to the number per minute and convert the times
> During normal business hours on the east coast, calls to the toll-free reservation number of the Nite Time Inn arrive at a rate of 5 per minute. It has been determined that the number of calls per minute can be described by the Poisson distribution. Find
> Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. Find the probability that a call tak
> Discuss the differences among decision making under certainty, decision making under risk, and decision making under uncertainty.
> For each of the following F values, determine whether the probability indicated is greater than or less than 1%: (a) P(F5,4 > 14) (b) P(F6,3 > 30) (c) P(F10,12 > 4.2) (d) P(F2,3 > 35) (e) P(F2,3 < 35)
> For each of the following F values, determine whether the probability indicated is greater than or less than 5%: (a) P(F3,4 > 6.8) (b) P(F7,3 > 3.6) (c) P(F20,20 > 2.6) (d) P(F7,5 > 5.1) (e) P(F7,5 < 5.1)
> The Jamis Corporation is involved with waste management. During the past 10 years, it has become one of the largest waste disposal companies in the Midwest, serving primarily Wisconsin, Illinois, and Michigan. Bob Jamis, president of the company, is cons
> Coren Chemical, Inc., develops industrial chemicals that are used by other manufacturers to produce photographic chemicals, preservatives, and lubricants. One of their products, K-1000, is used by several photographic companies to make a chemical that is
> A mortgage lender attempted to increase its business by marketing its subprime mortgage. This mortgage is designed for people with a less-than-perfect credit rating, and the interest rate is higher to offset the extra risk. In the past year, 20% of these
> Burger City is a large chain of fast-food restaurants specializing in gourmet hamburgers. A mathematical model is now used to predict the success of new restaurants based on location and demographic information for that area. In the past, 70% of all rest
> Policy Pollsters is a market research firm specializing in political polls. Records indicate in past elections, when a candidate was elected, Policy Pollsters had accurately predicted this 80% of the time and was wrong 20% of the time. Records also show,
> Market Researchers, Inc., has been hired to perform a study to determine if the market for a new product will be good or poor. In similar studies performed in the past, whenever the market actually was good, the market research study indicated that it wo
> A particular test for the presence of steroids is to be used after a professional track meet. If steroids are present, the test will accurately indicate this 95% of the time. However, if steroids are not present, the test will indicate this 90% of the ti
> Jim Sellers has been able to estimate his utility for a number of different values. He would like to use these utility values in making the decision in Problem 3-44: U(-$80,000) = 0, U(-$65,000) = 0.5, U(-$60,000) = 0.55, U(-$20,000) = 0.7, U(-$5,000) =
> What is an alternative? What is a state of nature?
> Jim Sellers is thinking about producing a new type of electric razor for men. If the market were favorable, he would get a return of $100,000, but if the market for this new type of razor were unfavorable, he would lose $60,000. Since Ron Bush is a good
> Patients arrive at the emergency room of Costa Valley Hospital at an average of 5 per day. The demand for emergency room treatment at Costa Valley follows a Poisson distribution. (a) Using Appendix C, compute the probability of exactly 0, 1, 2, 3, 4, an
> A new integrated computer system is to be installed worldwide for a major corporation. Bids on this project are being solicited, and the contract will be awarded to one of the bidders. As a part of the proposal for this project, bidders must specify how
> The time to complete a construction project is normally distributed with a mean of 60 weeks and a standard deviation of 4 weeks. (a) What is the probability the project will be finished in 62 weeks or less? (b) What is the probability the project will be
> Armstrong Faber produces a standard number-two pencil called Ultra-Lite. Since Chuck Armstrong started Armstrong Faber, sales have grown steadily. With the increase in the price of wood products, however, Chuck has been forced to increase the price of th
> Susan Williams has been the production manager of Medical Suppliers, Inc., for the past 17 years. Medical Suppliers, Inc., is a producer of bandages and arm slings. During the past 5 years, the demand for No-Stick bandages has been fairly constant. On av
> An industrial oven used to cure sand cores for a factory manufacturing engine blocks for small cars is able to maintain fairly constant temperatures. The temperature range of the oven follows a normal distribution with a mean of 450 ℉ and a standard devi
> The Lubricant is an expensive oil newsletter to which many oil giants subscribe, including Ken Brown (see Problem 3-17 for details). In the last issue, the letter described how the demand for oil products would be extremely high. Apparently, the American
> The Technically Techno company has several patents for a variety of different flash memory devices that are used in computers, cell phones, and a variety of other things. A competitor has recently introduced a product based on technology very similar to
> Describe what is involved in the decision process.
> Although Ken Brown (discussed in Problem 3-17) is the principal owner of Brown Oil, his brother Bob is credited with making the company a financial success. Bob is vice president of finance. Bob attributes his success to his pessimistic attitude about bu
> The game of roulette is popular in many casinos around the world. In Las Vegas, a typical roulette wheel has the numbers 1–36 in slots on the wheel. Half of these slots are red, and the other half are black. In the United States, the roulette wheel typic
> There are 10 questions on a true–false test. A student feels unprepared for this test and randomly guesses the answer for each of these. (a) What is the probability that the student gets exactly 7 correct? (b) What is the probability that the student get
> What are the expected value and variance of the following probability distribution? RANDOM VARIABLE X PROBABILITY 1 …………………………………………………….. 0.05 2 …………………………………………………….. 0.05 3 …………………………………………………….. 0.10 4 …………………………………………………….. 0.10 5 …………………………………………
> The North side rifle team has two markspersons, Dick and Sally. Dick hits a bull’s-eye 90% of the time, and Sally hits a bull’s-eye 95% of the time. (a) What is the probability that either Dick or Sally or both will hit the bull’s-eye if each takes one
> The schedule for the Killers next year is as follows (refer to Problem 2-24): Game 1: The Machos Game 2: Mama’s Boys Problem 2-24: The Boston South Fifth Street Softball League consists of three teams: Mama’s Boys, te
> Compute the probability of “loaded die given that a 3 was rolled,” as shown in the example in Section 2.3, this time using the general form of Bayes’ Theorem from Equation 2-5 Theorem from Equation 2-5: P(A/B) = P(B/A) P(A) P(B/A)P(A) + P(B/A′)P(A′)
> In a sample of 1,000 representing a survey from the entire population, 650 people were from Lake town, and the rest of the people were from River City. Out of the sample, 19 people had some form of cancer. Thirteen of these people were from Lake town. (a
> Bismarck Manufacturing intends to increase capacity through the addition of new equipment. Two vendors have presented proposals. The fixed cost for proposal A is $65,000 and for proposal B, $34,000. The variable cost for A is $10 and for B, $14. The reve
> Zoe Garcia is the manager of a small office-support business that supplies copying, binding, and other services for local companies. Zoe must replace a worn-out copy machine that is used for black-and white copying. Two machines are being considered, and
> How is a utility curve used in selecting the best decision for a particular problem?
> WTVX, Channel 6, is located in Eugene, Oregon, home of the University of Oregon. The station was owned and operated by George Wilcox, a former Duck (University of Oregon football player). Although there were other television stations in Eugene, WTVX was
> The Boston South Fifth Street Softball League consists of three teams: Mama’s Boys, team 1; the Killers, team 2; and the Machos, team 3. Each team plays the other teams just once during the season. The win–loss record
> Ace Machine Works estimates that the probability its lathe tool is properly adjusted is 0.8. When the lathe is properly adjusted, there is a 0.9 probability that the parts produced pass inspection. If the lathe is out of adjustment, however, the probabil
> The lost Israeli soldier mentioned in Problem 2-21 decides to rest for a few minutes before entering the desert oasis he has just found. Closing his eyes, he dozes off for 15 minutes, wakes, and walks toward the center of the oasis. The first person he s
> The oasis outpost of Abu Ilan, in the heart of the Negev desert, has a population of 20 Bedouin tribesmen and 20 Farima tribesmen. El Kamin, a nearby oasis, has a population of 32 Bedouins and 8 Farima. A lost Israeli soldier, accidentally separated from
> David Mashley teaches two undergraduate statistics courses at Kansas College. The class for Statistics 201 consists of 7 sophomores and 3 juniors. The more advanced course, Statistics 301, has 2 sophomores and 8 juniors enrolled. As an example of a busin
> The Springfield Kings, a professional basketball team, has won 12 of its last 20 games and is expected to continue winning at the same percentage rate. The team’s ticket manager is anxious to attract a large crowd to tomorrow’s game but believes that dep
> Last year, at Northern Manufacturing Company, 200 people had colds during the year. One hundred fifty five people who did no exercising had colds, and the remainder of the people with colds were involved in a weekly exercise program. Half of the 1,000 em
> Ever tight, a leading manufacturer of quality nails, produces 1-, 2-, 3-, 4-, and 5-inch nails for various uses. In the production process, if there is an overrun or the nails are slightly defective, they are placed in a common bin. Yesterday, 651 of the
> An urn contains 8 red chips, 10 green chips, and 2 white chips. A chip is drawn and replaced, and then a second chip drawn. What is the probability of (a) a white chip on the first draw? (b) a white chip on the first draw and a red on the second? (c) tw
> A silver dollar is flipped twice. Calculate the probability of each of the following occurring: (a) a head on the first flip (b) a tail on the second flip given that the first toss was a head (c) two tails (d) a tail on the first and a head on the secon
> Briefly discuss how a utility function can be assessed. What is a standard gamble, and how is it used in determining utility values?
> A student taking Management Science 301 at East Haven University will receive one of the five possible grades for the course: A, B, C, D, or F. The distribution of grades over the past 2 years is as follows: GRADE NUMBER OF STUDENTS A …………………………………….… 8
> Students in a management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes, as well as the final averages for the same students. Some of these gra
> Using computer software, find the least-squares regression line for the data in Problem 4-10. Based on the F test, is there a statistically significant relationship between the demand for guitars and the number of YouTube views? Problem 4-10: The operat
> Using the data in Problem 4-10, test to see if there is a statistically significant relationship between sales and YouTube views at the 0.05 level of significance. Use the formulas in this chapter and Appendix D. Problem 4-10: The operations manager of
> The operations manager of a musical instrument distributor feels that demand for a particular type of guitar may be related to the number of YouTube views for a music video by the popular rock group Marble Pumpkins during the preceding month. The manager
> Raptor Fuels produces three grades of gasoline— Regular, Premium, and Super. All of these are produced by blending two types of crude oil—Crude A and Crude B. The two types of crude contain specific ingredients that he
> Working with chemists at Virginia Tech and George Washington Universities, landscape contractor Kenneth Golding blended his own fertilizer, called “Golding-Grow.” It consists of four chemical compounds: C-30, C-92, D-21, and E-11. The cost per pound for
> Modem Corporation of America (MCA) is the world’s largest producer of modem communication devices. MCA sold 9,000 of the regular model and 10,400 of the smart (“intelligent”) model this September. Its
> Outdoor Inn (see Problem 7-41) expanded its tent making operations later in the year. While still making the Double Inn tent, it is also making a larger tent, the Family Rolls, which has four rooms. The company can produce up to a combined total of 280 t
> Outdoor Inn, a camping equipment manufacturer in southern Utah, is developing a production schedule for a popular type of tent, the Double Inn. Orders have been received for 180 of these to be delivered at the end of this month, 220 to be delivered at th
> What is the purpose of Bayesian analysis? Describe how you would use Bayesian analysis in the decision-making process.
> The Weinberger Electronics Corporation manufactures four highly technical products that it supplies to aerospace firms that hold NASA contracts. Each of the products must pass through the following departments before being shipped: wiring, drilling, asse
> The Feed ’N Ship Ranch fattens cattle for local farmers and ships them to meat markets in Kansas City and Omaha. The owners of the ranch seek to determine the amounts of cattle feed to buy so that minimum nutritional standards are satis
> Refer to the Bhavika Investments (Problem 7-37) situation once again. It has been decided that, rather than minimizing risk, the objective should be to maximize return while placing a restriction on the amount of risk. The average risk should be no mo
> Bhavika Investments, a group of financial advisors and retirement planners, has been requested to provide advice on how to invest $200,000 for one of its clients. The client has stipulated that the money must be put into either a stock fund or a money ma
> The three princes of Serendip Went on a little trip. They could not carry too much weight; More than 300 pounds made them hesitate. They planned to the ounce. When they returned to Ceylon They discovered that their supplies were just about gone When, wha
> Graphically solve the following problem: Maximize profit = 8X1 + 5X2 subject to X1 + X2 ≤ 10 X1 ≤ 6 X1, X2 Ú 0 (a) What is the optimal solution? (b) Change the right-hand side of constraint 1 t
> The computer output on the next page is for a product mix problem in which there are two products and three resource constraints. Use the output to help you answer the following questions. Assume that you wish to maximize profit in each case. (a) How ma
> Consider the LP formulation given in Problem 7-31. If the second constraint is changed from 2X + 3Y ≤ 240 to 2X + 4Y ≤ 240, what effect will this have on the optimal solution? Problem 7-31: Consider the following LP problem: Maximize profit = 5X + 6 Y
> Consider the following LP problem: Maximize profit = 5X + 6 Y subject to 2X + Y ≤ 120 2X + 3Y ≤ 240 X, Y ≥ 0 (a) What is the optimal solution to this problem? Solve it graphically. (b) If a technical breakthrough occurred that raised the
> Graph the following LP problem and indicate the optimal solution point: Maximize profit = $3X + $2Y subject to 2X + Y ≤ 150 2X + 3Y ≤ 300 (a) Does the optimal solution change if the profit per unit of X changes to $4.50? (b) What happens if the
> Give an example of a good decision that you made that resulted in a bad outcome. Also give an example of a bad decision that you made that had a good outcome. Why was each decision good or bad?
> Consider the following four LP formulations. Using a graphical approach, determine (a) which formulation has more than one optimal solution. (b) which formulation is unbounded. (c) which formulation has no feasible solution. (d) which formulation is cor
> The seasonal yield of olives in a Piraeus, Greece, vineyard is greatly influenced by a process of branch pruning. If olive trees are pruned every two weeks, output is increased. The pruning process, however, requires considerably more labor than permitti
