Question: Modify PC Tech’s product mix model

> The U.S. government wants to determine whether immigrants should be tested for a contagious disease, and it is planning to base this decision on financial considerations. Assume that each immigrant who is allowed to enter the United States and has the di

> A company is considering whether to market a new product. Assume, for simplicity, that if this product is marketed, there are only two possible outcomes: success or failure. The company assesses that the probabilities of these two outcomes are p and 1 2

> A customer has approached a bank for a $100,000 one-year loan at an 8% interest rate. If the bank does not approve this loan application, the $100,000 will be invested in bonds that earn a 6% annual return. Without additional information, the bank believ

> Referring to the landowner’s decision problem in Problem 32, suppose now that, at a cost of $90,000, the landowner can request a soundings test on the site where natural gas is believed to be present. The company that conducts the soundings concedes that

> The fixed cost of $6 million in the Acme problem is evidently not large enough to make Acme abandon the product at the current time. How large would the fixed cost need to be to make the abandon option the best option? Explain how the decision tree, espe

> Model 8 has fairly high profit margins, but it isn’t included at all in the optimal mix. Use SolverTable, along with some experimentation on the correct range, to find the (approximate) selling price required for model 8 before it enters the optimal prod

> Yearly automobile inspections are required for residents of the state of Pennsylvania. Suppose that 12% of all inspected cars in Pennsylvania have problems that need to be corrected. Unfortunately, Pennsylvania state inspections fail to detect these prob

> Consider a population of 3000 people, 1400 of whom are men. Assume that 700 of the women in this population earn at least $60,000 per year, and 500 of the men earn less than $60,000 per year. a. What is the probability that a randomly selected person fro

> You have sued your employer for damages suffered when you recently slipped and fell on an icy surface that should have been treated by your company’s physical plant department. Your injury was sufficiently serious that you, in consultation with your atto

> Two construction companies are bidding against one another for the right to construct a new community center building in Bloomington, Indiana. The first construction company, Fine Line Homes, believes that its competitor, Buffalo Valley Construction, wil

> A buyer for a large department store chain must place orders with an athletic shoe manufacturer six months prior to the time the shoes will be sold in the department stores. The buyer must decide on November 1 how many pairs of the manufacturer’s newest

> An investor with $10,000 available to invest has the following options: (1) he can invest in a risk free savings account with a guaranteed 3% annual rate of return; (2) he can invest in a fairly safe stock, where the possible annual rates of return are 6

> Techware Incorporated is considering the introduction of two new software products to the market. The company has four options regarding these products: introduce neither product, introduce product 1 only, introduce product 2 only, or introduce both prod

> A local energy provider offers a landowner $180,000 for the exploration rights to natural gas on a certain site and the option for future development. This option, if exercised, is worth an additional $1,800,000 to the landowner, but this will occur only

> Carlisle Tire and Rubber, Inc., is considering expanding production to meet potential increases in the demand for one of its tire products. Carlisle’s alternatives are to construct a new plant, expand the existing plant, or do nothing in the short run. T

> The SweetTooth Candy Company knows it will need 10 tons of sugar six months from now to implement its production plans. The company has essentially two options for acquiring the needed sugar. It can either buy the sugar at the going market price when it

> Create a two-way SolverTable for the product mix model, where total profit is the only output and the two inputs are the testing line 1 hours and testing line 2 hours available. Let the former vary from 4000 to 6000 in increments of 500, and let the latt

> Some decision makers prefer decisions with low risk, but this depends on how risk is measured. As we mentioned in this section, variance is one measure of risk, but it includes both upside and downside risk. That is, an outcome with a large positive payo

> Starting with the finished version, change the fixed marketing cost to $4000 (really $4 million) in cell B5, and change the decision criterion to “maximize expected utility,” using an exponential utility function with risk tolerance $5000 (really $5 mill

> Starting with the finished version, change the decision criterion to “maximize expected utility,” using an exponential utility function with risk tolerance $5000 (really $5 million). Display certainty equivalents on the tree. a. Keep doubling the risk to

> You saw how Acme prefers to abandon the product when the risk tolerance in cell B12 is $5000 (really $5 million). This is despite the fact that the EMV from continuing with the product is well above 0. Using this same risk tolerance, experiment with the

> Using the finished version of the file, use a data table to perform a sensitivity analysis on the risk tolerance. Specifically, let the risk tolerance in cell B12 vary from $10,000 to $100,000 and keep track of two outputs in the data table, the TRUE/FAL

> Explain what it means in general when we say a risk-averse decision maker is willing to give up some EMV to avoid risk? How is this apparent in certainty equivalents of gambles?

> In the original OJ Simpson trial, it was accepted that OJ had battered his wife. OJ’s lawyer tried to negate the impact of this information by stating that in a one-year period, only 1 out of 2500 battered women are murdered, so the fact that OJ battered

> The terms prior and posterior are relative. Assume that the test has been performed, and the outcome is positive, which leads to the posterior probabilities shown. Now assume there is a second test, independent of the first, that can be used as a follow-

> The model has only two market outcomes, good and bad, and two corresponding predictions, good and bad. Modify the decision tree by allowing three outcomes and three predictions: good, fair, and bad. You can change the inputs to the model (monetary values

> A technological failure implies that the game is over—the product must be abandoned. Change the problem so that there are two levels of technological failure, each with probability 0.1. In the first level, Acme can pay a further development cost D to fix

> Use SolverTable to run a sensitivity analysis on the cost per assembling labor hour, letting it vary from $5 to $20 in increments of $1. Keep track of the computers produced in row 21, the hours used in the range B26:B28, and the total profit. Discuss yo

> If you examine the decision tree (or any other decision trees from PrecisionTree), you will see two numbers (in blue font) to the right of each end node. The bottom number is the combined monetary value from following the corresponding path through the t

> For the decision problem in Figure 9.1, use data tables to perform the following sensitivity analyses. The goal in each is to see whether decision 1 continues to have the largest EMV. In each part, provide a brief explanation of the results. a. Let the p

> Suppose you are tested to see if you have a rare disease. Assume that if you have the disease, your test will always come back positive, but if you do not have the disease, there is still a 0.001 chance that you will test positive. In reality, only 1 of

> Starting with the finished version of the file, change the fixed cost in cell B5 to $4000. Change the probabilities in cells B9 (make it smaller), B14 (make it larger), and B15 (make it smaller) in some systematic way (you can choose the details) and, fo

> Starting with the finished version of the file for Example, change the fixed cost in cell B5 to $4000. Then get back into PrecisionTree’s One-Way Sensitivity Analysis dialog box and add three more inputs. (These will be in addition to the two inputs alre

> The finished version of the file for Example contains two “Strategy B9” sheets. Explain what each of them indicates and how they differ.

> In using Bayes’ rule for the presence of a disease, we assumed that there are only two test results, positive or negative. Suppose there is another possible test result, “maybe.” The 2 * 2 range B9:C10 in the file should now be replaced by a 2 * 3 range,

> In the file Bayes Rule for Disease.xlsx, explain why the probabilities in cells B9 and B10 (or those in cells C9 and C10) do not necessarily sum to 1, but why the probabilities in cells B9 and C9 (or those in cells B10 and C10) do necessarily sum to 1.

> Use a two-way PrecisionTree sensitivity analysis to examine the changes in both of the two previous problems simultaneously. Let the probability of technological success vary from 0.6 to 0.9 in increments of 0.05, and let the fixed cost of development va

> The fixed costs are split $4 million for development and $2 million for marketing. Perform a sensitivity analysis where the sum of these two fixed costs remains at $6 million but the split changes. Specifically, let the fixed cost of development vary fro

> In the product mix model it makes sense to change the maximum sales constraint to a “minimum sales” constraint, simply by changing the direction of the inequality Then the input values in row 23 can be considered customer demands that must be met. Make t

> Acme’s probability of technological success, 0.8, is evidently large enough to make “continue development” the best decision. How low would this probability have to be to make the opposite decision best?

> Use PrecisionTree to solve problem 7 of the previous section. Data from Problem 7: Sometimes a “single-stage” decision can be broken down into a sequence of decisions, with no uncertainty resolved between these decisions. Similarly, uncertainty can some

> Several decision criteria besides EMV are suggested in the section. For each of the following criteria, rank all three decisions in Figure 9.1 from best to worst. a. Look only at the worst possible outcome for each decision. b. Look only at the best poss

> You are given the following information concerning how a change in sales force effort impacts sales: ■ A 50% cut in sales force effort reduces sales to 48% of its current value. ■ Sales force effort of 0 reduces sales to 15% of its current value. ■ A 50%

> In the lawn mower production problem, experiment with the penalty cost for unsatisfied pickups in week 1. If this cost is sufficiently small, does the company ever produce fewer than seven models in week 1 and allow some week 1 pickups to be unsatisfied?

> In the lawn mower production problem, the model changeover cost dominates in the optimal objective value. Is this because we assumed such a large unit penalty cost, 200, for each model changeover? Explore this question by changing this unit penalty cost

> In the truck-loading problem, we assumed that any product could be loaded into any compartment. Suppose the following are not allowed: product 1 in compartment 2, product 2 in compartment 1, and product 3 in compartment 4. Modify the model appropriately,

> Based on Schrage (1997). The file P08_05.xlsx lists the size of the four main markets for Excel, Word, and the bundle of Excel and Word. (We assume that Microsoft is willing to sell Excel or Word separately, and it is willing to sell a package with Excel

> Suppose you are the new supply manager at FedEx. You need to choose three hubs for the company. Each of 28 cities will send all of its outgoing packages to one of the hubs. The packages will then be sent from the hubs to their final destinations. The fil

> Determine the optimal pricing policy if Menthos are sold in only a one-pack or a six-pack.

> A company has nine jobs that must be assigned to three ordered workstations. The file P08_39.xlsx lists the times required for each job, which are independent of the workstations they are assigned to. It also lists precedence relationships between the jo

> Based on Meneses et al. (2004). A string is a list of characters such as “1differ%”. The length of the string is the number of characters in the string. The distance between two strings is the number of positions in which the two strings differ. For exam

> A common approach to clustering is called multidimensional scaling (MDS). To apply MDS, we rank each pair of objects we want to cluster from least similar (higher number) to most similar (lower number). For example, in the file, we compared the similarit

> An important problem in manufacturing is the assembly line balancing problem. When setting up a manufacturing line, activities must be assigned to workstations. The maximum time spent at a workstation is called the cycle time. Minimizing the cycle time t

> Assume that a consumer’s purchase decision on an electric razor is based on four attributes, each of which can be set at one of three levels (1, 2, or 3). Using conjoint analysis (a type of analysis used in marketing research), our analysts have divided

> Suppose you are the ad manager for Fox NFL football. Thirty bids for ads on today’s game between the Packers and the Colts have been submitted. Information on these ads is given in the file P08_34.xlsx. For example, ad 1 is 23 seconds in length and will

> A steel manufacturer needs to cool 17 pieces of steel. The weight and due date for each piece are listed in the file P08_33.xlsx. Processing and cooling a batch in the furnace takes five minutes regardless of the weight in the furnace. The furnace can ha

> You are the Democratic campaign manager for the state of Indiana. There are 15 fairly large cities in the state of Indiana. The numbers of Democrats and Republican voters in these cities (in thousands) are listed in the file P08_32.xlsx. The Democrats co

> Xerox is trying to determine how many maintenance centers are needed in the mid-Atlantic states. Xerox earns $500 profit (excluding the cost of running maintenance centers) on each copier sale. The sales of copiers in each major market (Boston, New York,

> Ten data sets must be assigned for storage to one of three disk drives. Each disk drive can store 150 GB (about 150,000 MB). The sizes of the data sets (in MB) are listed in the file P08_30.xlsx. When many people access a disk drive, there is a significa

> Other sensitivity analyses besides those discussed could be performed on the product mix model. Use SolverTable to perform each of the following. In each case keep track of the values in the decision variable cells and the objective cell, and discuss you

> Determine the best pricing policy if quantity discounts with a single-price breakpoint are used.

> Bus 99 serves towns 1 through 10. We assume that town k is |k – j| miles from town j. The numbers of people in the towns who want to take the bus each hour are listed in the file P08_29.xlsx. Bus 99 will make two stops and anyone who wants to take the bu

> During the next 12 months, the amounts of electric power needed (in thousands of kwh) are listed in the file. This power can be supplied using four generators. The generating capacity (in thousands of kwh), the operating cost, the startup cost, and the s

> A Wall Street firm is trying to package nine mortgages for sale. The sizes of the mortgages (in thousands of dollars) are listed in the file. To be sold, each package must consist of at least $1,000,000 in mortgages. What is the largest number of package

> Music radio WABC has commercials of the following lengths (in seconds): 15, 15, 20, 25, 30, 35, 40, 57. The commercials must be assigned to 60-second breaks. What is the fewest number of breaks that are needed to air all of the commercials?

> The file contains quarterly revenue for a sporting goods company over an 8-year period. It also contains quarterly “indicator” variables Q1, Q2, and Q3. Here Q1 is 1 for the first quarter of a fiscal year (July–September) and 0 otherwise. Q2 and Q3 are d

> Cook County needs to build two hospitals. There are nine cities where the hospitals can be built. The number of hospital visits made annually by the inhabitants of each city and the x and y coordinates of each city are listed in the file P08_24.xlsx. To

> The costs of producing product A, product B, or products A and B bundled together are $50, $90, and $140, respectively. The file P08_23.xlsx lists the sizes of the three market segments for these products and how much each of the segments is willing to p

> Eight students need to be assigned to four dorm rooms (two students to a room) at State University. Based on incompatibility measures, the “cost” incurred if two students room together is shown in the file. How should these students be assigned to rooms

> Nine jobs need to be completed within eight weeks. The number of weeks required to complete each job is given in the file P08_21.xlsx. For example, job 2 requires five weeks. Each job requires 40 hours of labor per week. Each week, 160 hours of regular t

> In a production scheduling problem like Pigskin’s, suppose the company must produce several products to meet customer demands. Would it suffice to solve a separate model for each product, as we did for Pigskin, or would one big model for all products be

> Fourteen jobs must be assigned to one of three identical machines. The goal is to minimize the total time needed to complete all 14 jobs. The machine capacities and times needed for the jobs are given in file P08_20.xlsx. For example, job 8 requires thre

> Modify the function in Example 8.1 so that it becomes f(x) = x sin(x) for 0 ≤ x ≤ 30. (Here, sin(x) is the sine function from trigonometry. You can evaluate it with Excel’s SIN function.) Plot a lot of points from 0 to 30 to see what the graph of this fu

> The 30 teams in the NBA are each assigned to one of six divisions, where each division has five teams. Suppose the goal is to assign the teams to divisions so that the average distance among teams in the divisions is minimized. In other words, the goal i

> You are operating a Web site to match up sellers and buyers of a product. 35 sellers and 35 buyers have input their reservation prices, as listed in the file. For example, buyer 1 is willing to pay up to $8 for an item, and seller 1 is willing to accept

> Repeat Problem 15, but now assume there is a setup time for changing from any job to another job, and this setup time can depend on the jobs. For example, the setup time when changing from job 2 to job 4 can be different from the setup time when changing

> The traveling salesperson problem is notoriously difficult when the number of cities is even of moderate size. The file contains two sheets, one with a distance matrix for a 30-city problem and the other with a distance matrix for a 45-city problem. See

> An important problem in operations management is the job sequencing problem. Actually, there are many versions of this problem, but they all basically attempt to find the proper sequencing of jobs on a machine. Here is one version of the problem. There a

> Continuing the previous problem, determine the portfolio that minimizes the chance that you will lose money during any month, subject to a lower bound constraint on your expected monthly return. (The lower bound will depend on your data. It must not be a

> Visit biz.yahoo.com/r/. Under Research Tools, click on Historical Quotes, and then download the monthly returns on at least four stocks for the preceding 60 months. Use this data to determine the portfolio that maximizes the chance of beating the S&P 500

> Sales of a product over time often follow an S-shaped curve. Two functions that yield S-shaped curves are the Pearl (or logistic) curve Y = L / + ae-bt and the Gompertz curve Y = Le-be-kt Here, Y is annual sales, t is time (in years), L is the upper lim

> In a typical production scheduling model like Pigskin’s, if there are no production capacity constraints—the company can produce as much as it needs in any time period—but there are storage capacity constraints and demand must be met on time, is it possi

> The adoption level of a new product can often be modeled as an S-shaped curve called the Pearl (or logistic) curve. The equation of this curve is Y = L / + ae-bt where Y is the adoption level, L is an (unknown) upper limit on adoptions, t is time (in ye

> The file contains per capita data on annual advertising and annual unit sales in different regions of the country. Determine an S-shaped curve as described by Equation that can be used to determine how advertising influences sales.

> Modify the function in Example 8.1 so that it becomes f(x) = (x - 1)(x - 2)(x - 3)(x - 4)(x - 5)(x - 6)(x - 7) for 1 ≤ x ≤ 7. Plot a lot of points from 1 to 7 to see what the graph of this function looks like. Then use GRG Nonlinear Solver to find its ma

> In the complementary-product pricing model, the elasticity of demand for suits is currently 22.5. Use SolverTable to see how the optimal price of suits and the optimal profit vary as the elasticity varies from 22.7 to 21.8 in increments of 0.1. Are the r

> Your family owns a large farm that can grow wheat, corn, cotton, alfalfa, barley, pears, and apples. Each product requires a certain amount of labor each month and a certain number of hours of machine time. You have just studied portfolio optimization an

> UE is going to invest $400 million to acquire companies in the auto and/or electronics industry. How would you apply portfolio optimization to determine which companies should be purchased?

> Consider the sports ratings model. If you were going to use the approach used there to forecast future sports contests, what problems might you encounter early in the season? How might you resolve these problems?

> Consider the sports ratings model. If you were going to give more recent games more weight, how might you determine whether the weight given to a game from k weeks ago should be, say, (0.95)k or (0.9)k?

> For the aggregate planning example, is it likely that the cost per worker of changing the size of the workforce during a month would be constant (as we assumed)? How could an NLP model account for a situation in which the cost per worker of changing the

> For the oil blending example, discuss where you think the assumptions of a linear model are most likely to break down. How might an NLP model look in this situation?

> In a typical product mix model, where a company must decide how much of each product to produce to maximize profit, there are sometimes customer demands for the products. We used upper-bound constraints for these: Don’t produce more than you can sell. Wo

> In some ordering problems, like the one for Sam’s Bookstore, whenever demand exceeds existing inventory, the excess demand is not lost but is filled by expedited orders—at a premium cost to the company. Change Sam’s model to reflect this behavior. Assume

> For the product mix examples, discuss where you think the assumptions of a linear model are most likely to break down. How might an NLP model look in this situation?

> In the exchange rate model, we found that the optimal unit revenue, when converted to dollars, is $85.71. Now change the problem so that the company is selling in Japan, not the United Kingdom. Assume that the exchange rate is 0.00965 ($/¥) and that the

> Your company is about to market a new golf club. You have convened a focus group of 100 golfers and asked them to compare your club to the clubs produced by your competitors. You have found, for example, that 30 customers in the focus group would purchas

> A triangle has a 5-inch side and a 12-inch side. To maximize the area of the triangle what should the third side be? Can you generalize this result?

> You can swim two miles per hour and run six miles per hour. You are walking north along South Beach and see someone drowning half a mile out in the ocean and one mile north of you. What combination of running and swimming is the quickest way to reach the

> City B is 10 miles downstream from city A. City A is 5 miles south of the river, and city B is 20 miles north of the river. The river is two miles wide. Where should a bridge be built across the river to make the travel distance between cities A and B as