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practical management science
Questions and Answers of
Practical Management Science
Modify Example 12.9 so that the portfolio now contains 100 shares of stock and one put option on the stock with the same parameters as in the example.You can assume that the price of an option is
A European put option allows an investor to sell a share of stock at the exercise price on the exercise data.For example, if the exercise price is $48, and the stock price is $45 on the exercise
Referring to the retirement example in Example 12.7, rerun the model for a planning horizon of 10 years;15 years; 25 years. For each, try to find the set of investment weights that maximize the VAR
Modify the model from Example 12.7 so that you use only the years 1970 to 2001 of historical data. Run the simulation for the same three sets of investment weights. Comment on whether your results
The simulation output from Example 12.7 indicates that an investment heavy in stocks produces the best results. Would it be better to invest entirely in stocks?Find out by rerunning the simulation.
Then comment on the differences, if any, between your simulation results and those in the example.
Run the retirement model from Example 12.7 with a damping factor of 1.0 (instead of 0.98), again using the same three sets of investment weights. Explain in words what it means, in terms of the
In the cash balance model from Example 12.6, is the$250,000 minimum cash balance requirement really“costing” the company very much? Find out by rerunning the simulation with minimum required cash
In the cash balance model from Example 12.6, the timing is such that some receipts are delayed by 1 or 2 months, and the payments for materials and labor must be made a month in advance. Change the
Rerun the new car simulation from Example 12.5, but now use the RISKSIMTABLE function appropriately to simulate discount rates of 7.5%, 10%, 12.5%, and 15%. Comment on how the outputs change as the
Rerun the new car simulation from Example 12.5 but now introduce uncertainty into the fixed development cost. Let it be triangularly distributed with parameters$1.2 billion, $1.3 billion, and $1.7
In the simulation of Deming’s funnel experiment, the@RISK outputs show how tampering leads to poor results, at least in terms of the mean and standard deviation of the distance of the final drop
In the drug production example, Example 12.3, suppose we want to run 5 simulations, where we vary the probability of passing inspection from 0.6 to 1.0 in increments of 0.1. Use the RISKSIMTABLE
Do you always get this answer? Find out by (1) running the simulation 10 more times, each with 1000 iterations, and finding the 95th percentile and corresponding date in each, and(2) running the
In the drug production example, Example 12.3, we commented on the 95th percentile on days required in cell I35 and the corresponding date in cell J35. If the company begins production on this date,
See how sensitive the results in the warranty example, Example 12.2, are to the following changes. For each part, make the change indicated, run the simulation, and comment on any differences between
In the warranty example, Example 12.2, we introduced the gamma distribution to model the right skewness of the lifetime distribution. Experiment to see how the results change if you use the
Referring to Example 12.1, if the average bid for each competitor who bids stays the same, but their bids exhibit less variability, does Miller’s optimal bid increase or decrease? To study this
If the number of competitors in Example 12.1 doubles, how does the optimal bid change?
In Example 12.1, the possible profits vary from negative to positive for each of the 10 possible bids examined.a. For each of these, use @RISK’s RISKTARGET function to find the probability that
We are constantly hearing reports on the nightly news about natural disasters—droughts in Texas, hurricanes in Florida, floods in California, and so on. We often hear that one of these was the
A building contains 1000 light bulbs. Each bulb lasts at most 5 months. The company maintaining the building is trying to decide whether it is worthwhile to practice a “group replacement” policy.
Many people who are involved in a small auto accident do not file a claim because they are afraid their insurance premiums will be raised. Suppose that City Farm Insurance has three rates. If you
Big Hit Video must determine how many copies of a new video to purchase. Assume that the company’s goal is to purchase a number of copies that will maximize its expected profit from the video
In statistics, we often use observed data to test a hypothesis about a population or populations. The basic method uses the observed data to calculate a test statistic (a single number). If the
Note that each of these distributions is very nonnormal. Run each simulation with 10 values in each average, and run 1000 iterations to simulate 1000 averages. Create a histogram of the averages to
Simulation can be used to illustrate a number of results from statistics that are difficult to understand with nonsimulation arguments. One is the famous central limit theorem, which says that if you
At the beginning of each week, a machine is in one of four conditions: 1 excellent; 2 good; 3 average; 4 bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is $100, $90, $50,
ATax Saver Benefit (TSB) plan allows you to put money into an account at the beginning of the calendar year that can be used for medical expenses. This amount is not subject to federal tax—hence
United Electric (UE) sells refrigerators for $400 with a 1-year warranty. The warranty works as follows. If any part of the refrigerator fails during the first year after purchase, UE replaces the
If the set of numbers is 4, 3, 2, 4, the RANK function will return 1, 3, 4, 1.c. After using the RANK function, you should be able to determine whether at least two of the 30 people have the same
It is surprising (but true) that if 23 people are in the same room, there is about a 50% chance that at least two people will have the same birthday. Suppose you want to estimate the probability that
The file has the formulas you might expect for this situation entered in the range C20:G23. You can check how the RISKCORRMAT function has been used in these formulas. Just so that we have an@RISK
The annual return on each of four stocks for each of the next five years is assumed to follow a normal distribution, with the mean and standard deviation for each stock, as well as the correlations
If Target orders 200 jerseys, its cost is $27.00 per jersey. Every increment of 50 jerseys reduces the unit cost of a jersey by $1.35. For example, if the order quantity is from 250 jerseys to 299
Target is trying to decide how many Peyton Manning jerseys to order for the upcoming football season.The jerseys sell for $50, and Target believes that the demand at this price is normally
For example, if full-price demand is 2500, then at a 10% discount, customers would be willing to buy 1000 T-shirts. The unit cost of purchasing T-shirts depends on the number of T-shirts ordered, as
Demand at various discounts is assumed to be a multiple of full price demand.These multiples, for discounts of 10%, 20%, 40%, 50%, and 60% are, respectively, 0.4, 0.7, 1.1, 2, and
Dilbert’s Department Store is trying to determine how many Hanson T-shirts to order. Currently the shirts are sold for $21.00, but at later dates the shirts will be offered at a 10% discount, then
The contract between Jean Hudson and Lemington’s works as follows. At the beginning of the season, Lemington’s reserves x units of capacity. Lemington’s must take delivery for at least 0.8x
Lemington’s is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation
The average test score of those selected is the average of the scores that are at least 0.842. To determine this, use Excel’s DAVERAGE function. To do so, put the heading Score in cell A3, generate
Assume that all of your job applicants must take a test, and that the scores on this test are normally distributed.The “selection ratio” is the cutoff point you use in your hiring process. For
W. L. Brown, a direct marketer of women’s clothing, must determine how many telephone operators to schedule during each part of the day. W. L. Brown estimates that the number of phone calls
It is equally likely that annual unit sales for Widgetco’s widgets will be low or high. If sales are low (60,000), the company can sell the product for $10 per unit. If sales are high (100,000), a
A new edition of our management science textbook will be published a year from now. Our publisher currently has 2000 copies on hand and is deciding whether to do another printing before the new
If the prize is really behind door 3, Monty must open door 1.
If the prize is really behind door 1, Monty must open door
If the prize is really behind door 2, Monty is equally likely to open door 1 or door
You now have the opportunity to switch and choose door 1.Should you switch? Use a spreadsheet to simulate this situation 1000 times. For each replication, use an@RISK function to generate the door
Before you see whether the prize is behind door 2, host Monty Hall opens a door that has no prize behind it. To be specific, suppose that before door 2 is opened, Monty reveals that there is no prize
It is equally likely that the prize is behind any of the three doors. The two doors without a prize have nothing behind them. You randomly choose door
You have made it to the final round of “Let’s Make a Deal.” You know that there is $1 million prize behind one of the three doors: door 1, door 2, or door
Six months before its annual convention, the American Medical Association (AMA) must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $100 per room. The AMA
The Business School at State University currently has three parking lots, each containing 155 spaces. Two hundred faculty members have been assigned to each lot. On a peak day, an average of 70% of
The effect of the shapes of input distributions on the distribution of an output can depend on the output function. For this problem, assume there are 10 input variables. We want to compare the case
Suppose you are going to invest equal amounts in three stocks. The annual return from each stock is normally distributed with mean 0.01 (1%) and standard deviation 0.06. The annual return on your
This time, verify not only that the correlation between the two inputs is approximately 0.7, but also that the shapes of the two input distributions are approximately what they should be: normal for
Repeat Problem 23, but now make the second input variable triangularly distributed with parameters 50, 100, and
Repeat the previous problem, but make the correlation between the two inputs equal to 0.7. Explain how the results change.
When you use @RISK’s correlation feature to generate correlated random numbers, how can you verify that they are correlated? Try the following. Use the RISKCORRMAT function to generate two normally
Bottleco produces six-packs of soda cans. Each can is supposed to contain at least 12 ounces of soda. If the total weight in a six-pack is under 72 ounces, Bottleco is fined $100 and receives no
Although the normal distribution is a reasonable input distribution in many situations, it does have two potential drawbacks: (1) it allows negative values, even though they may be extremely
Do this for the discrete distributions given in the problem and then do it for normal distributions.For the normal case, assume that the regular demand is normally distributed with mean 9800 and
Use @RISK to analyze the sweatshirt situation in Problem
Use @RISK to determine the best order quantity, that is, the one with the largest mean profit.Using the statistics and/or graphs from @RISK, discuss whether this order quantity would be considered
In Problem 12, suppose that the demand for cars is normally distributed with mean 100 and standard deviation
Continuing the previous problem, assume as in Problem 11 that the damage amount is normally distributed with mean $3000 and standard deviation $750. Run @RISK with 5000 iterations to simulate the
In Problem 11, suppose that the damage amount is triangularly distributed with parameters 500, 1500, and 7000. That is, the damage in an accident can be as low as $500 or as high as $7000, the most
Your single output variable should be the sum of these three numbers.Verify with @RISK that the distribution of this output is approximately normal with mean 300 and variance 300 (hence, standard
If you add several normally distributed random numbers, the result is normally distributed, where the mean of the sum is the sum of the individual means, and the variance of the sum is the sum of the
But then an order of 200 calendars must also yield a larger expected profit than an order of 190 calendars.Why?)
In the Walton Bookstore example with a discrete demand distribution, explain why an order quantity other than one of the possible demands cannot maximize the expected profit. (Hint: Consider an order
A sweatshirt supplier is trying to decide how many sweatshirts to print for the upcoming NCAA basketball championships. The final four teams have emerged from the quarterfinal round, and there is now
In the Walton Bookstore example, suppose that Walton receives no money for the first 50 excess calendars returned but receives $2.50 for every calendar after the first 50 returned. Does this change
In August 2007, a car dealer is trying to determine how many 2008 cars to order. Each car ordered in August 2007 costs $10,000. The demand for the dealer’s 2008 models has the probability
Suppose you own an expensive car and purchase auto insurance. This insurance has a $1000 deductible, so that if you have an accident and the damage is less than $1000, you pay for it out of your
Continuing the preceding problem, suppose that another key uncertain input is the development time, which is measured in an integer number of months.For each of the following scenarios, choose an
A company is about to develop and then market a new product. It wants to build a simulation model for the entire process, and one key uncertain input is the development cost. For each of the
We all hate to bring change to a store. By using random numbers, we could eliminate the need for change and give the store and the customer a fair deal. This problem indicates how it could be done.a.
Then superimpose a normal distribution on this drawing, choosing the mean and standard deviation to match those from the triangular distribution. (Click on the Add Overlay button to get a choice of
Use @RISK to draw a triangular distribution with parameters 200, 300, and
Check your answer by using the BINOMDIST function appropriately in Excel.
Use @RISK to draw a binomial distribution that results from 50 trials with probability of success 0.3 on each trial, and use it to answer the following questions.a. What are the mean and standard
Then answer the following questions.a. What are the mean and standard deviation of this distribution?b. What are the 5th and 95th percentiles of this distribution?c. What is the probability that a
Use @RISK to draw a triangular distribution with parameters 300, 500, and
Then answer the following questions.a. What is the probability that a random number from this distribution is less than 450?b. What is the probability that a random number from this distribution is
Use @RISK to draw a normal distribution with mean 500 and standard deviation
Then answer the following questions.a. What are the mean and standard deviation of this distribution?b. What are the 5th and 95th percentiles of this distribution?c. What is the probability that a
Use @RISK to draw a uniform distribution from 400 to
Are the answers close to what they should be (as you learned in your statistics course)?c. Create a histogram of the random numbers using 10 to 15 categories of your choice. Does this histogram have
Then freeze these random numbers.a. Calculate the mean and standard deviation of these random numbers. Are they approximately what you would expect?b. Of these random numbers, what fraction is with k
Use Excel’s functions (not @RISK) to generate 1000 random numbers from a normal distribution with mean 100 and standard deviation
Use the RAND function and the Copy command to generate a set of 100 random numbers.a. What fraction of the random numbers are smaller than 0.5?b. What fraction of the time is a random number less
Based on Balson et al. (1992). An electric utility company is trying to decide whether to replace its PCB transformer in a generating station with a new and safer transformer. To evaluate this
The Ventron Engineering Company has just been awarded a $2 million development contract by the U.S. Army Aviation Systems Command to develop a blade spar for its Heavy Lift Helicopter program. The
The contract allows him to buy 100 shares of ABC stock at the end of March, April, or May at a guaranteed price of $50 per share. He can exercise this option at most once. For example, if he
Suppose an investor has the opportunity to buy the following contract, a stock call option, on March
Sarah Chang is the owner of a small electronics company.In 6 months, a proposal is due for an electronic timing system for the next Olympic Games. For several years, Chang’s company has been
Many men over 50 take the PSA blood test. The purpose of the PSA test is to detect prostate cancer early.Dr. Rene Labrie of Quebec conducted a study to determine whether the PSA test can actually
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