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practical management science

Questions and Answers of Practical Management Science

Suppose the current exchange rate is 100 yen per dollar. We currently sell 100 units of a product for 700 yen. The cost of producing and shipping the product to Japan is $5, and the current
Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company
A company produces widgets at plants 1 and 2. It costs 125x1/2 dollars to produce x units at plant 1 and 235x1/3 dollars to produce x units at plant 2. Each plant can produce up to 500 units. Each
If a monopolist produces qunits, she can charge 400 – 4q dollars per unit. The variable cost is $60 per unit.a. How can the monopolist maximize her profit?b. If the monopolist must pay a sales
It costs a company $12 to purchase an hour of labor and $15 to purchase an hour of capital. If L hours of labor and K units of capital are available, then 0.05L2/3 K1/3 machines can be
In the previous problem, what is the minimum-cost method of producing 100 machines? (Ignore the $10,000 budget constraint.)Data from Previous Problem:It costs a company $12 to purchase an hour of
The cost per day of running a hospital is 200,000 + 0.5x2 dollars, where x is the number of patients served per day. What number of patients served per day minimizes the cost per patient per day of
Two companies are producing widgets. It costs the first company q12 dollars to produce q1 widgets and the second company 0.5q22 dollars to produce q2 widgets. If a total of q widgets are
A company manufactures two products. If it charges price pi for product i, it can sell qi units of product i, where q1 = 60 – 3p1 + p2 and q2 = 80 – 2p2 + p1. It costs $5 to produce a unit
A brewing company has $100,000 to spend on advertising in four markets. The sales revenue (in thousands of dollars) that can be created in each market by spending xi thousand dollars in market i is
Q&H Company advertises during soap operas and football games. Each soap opera ad costs $50,000, and each football game ad costs $100,000. If S soap opera ads are purchased, they will be seen
A beer company has divided Bloomington into two territories. If the company spends x1 dollars on promotion in territory 1, it can sell 60x11/2 cases of beer there; and if it spends x2
A company uses raw material to produce two products. For $150, a unit of raw material can be purchased and processed into four units of product 1 and two units of product 2. If x1 units of
J&J has given you $12 million to spend on advertising Huggys diapers during the next 12 months. At the beginning of January, Huggys has a 30% market share. During any month, 10% of
Based on Kolesar and Blum (1973). Suppose that a company must service customers lying in an area of A square miles with n warehouses. Kolesar and Blum showed that when the warehouse(s) are
A company has five factories. The x- and y-coordinates of the location of each factory are given in the file P07_61.xlsx. The company wants to locate a warehouse at a point that minimizes the sum of
Monroe County is trying to determine where to place the county fire station. The locations of the county’s four major towns are as follows: (10, 20), (60, 20), (40, 30), and (80, 60) (Figure 7.50).
Consider three investments. You are given the following means, standard deviations, and correlations for the annual return on these three investments. The means are 0.12, 0.15, and 0.20. The standard
You have $1000 to invest in three stocks. Let R1 be the random variable representing the annual return on $1 invested in stock i. For example, if Ri = 0.12, then $1 invested in stock i at the
An oil company must determine how many barrels of oil to extract during each of the next two years. If the company extracts x1 million barrels during year 1, each barrel can be sold for 80 – x1
Suppose that you are hiring a weather forecaster to predict the probability that next summer will be rainy or sunny. The following suggests a method that can be used to ensure that the forecaster is
The cost of producing x units of a product during a month is x1/2 dollars. Show that the minimum-cost method of producing 40 units during the next two months is to produce all 40 units
Four items are for sale in the Dollar Value store. The product and sum of their prices is $7.11. What is the price of each item?
Most economies have a goal of maximizing the average consumption per period. Assume that during each year, an economy saves the same (to be determined) percentage S of its production.
Each morning during rush hour, 10,000 people want to travel from New Jersey to New York City. If a person takes the commuter train, the trip lasts 40 minutes. If x thousand people per
Kellpost Cereal Company sells four products: (1) Special L (a low-calorie, high-nutrition cereal); (2) Corn Bran (another low-calorie, high-nutrition cereal); (3) Admiral Smacks (a sugary cereal
Find the minimum perimeter rectangle having area 64 square feet. Can you generalize this result?
A cylindrical soda can has a volume of 20 cubic inches. What height and diameter minimize the surface area of the can? Can you generalize this result?
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
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
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?
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
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?
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?
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? How could an NLP model account for a situation in
Consider the sports ratings model in section 7.6. 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
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?
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
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
Visit http://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 file P08_18.xlsx contains information on the following items about 24 companies: EBITASS (earnings before income and taxes, divided by total assets), ROTC (return on total capital), and Group (1
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
Repeat Problem 20, 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
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 P08_23.xlsx. For example, buyer 1 is
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
Nine jobs need to be completed within eight weeks. The number of weeks required to complete each job is given in the file P08_26.xlsx. For example, job 2 requires three weeks. Each job
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
The costs of producing product A, product B, or products A and B bundled together are $50, $90, and $140, respectively. The file P08_28.xlsx lists the sizes of the three market segments for these
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_34.xlsx. Bus 99
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
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
Starting with the finished version of the file for Example 9.3, 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
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
Use Excel’s functions (not @RISK) to generate 1000 random numbers from a normal distribution with mean 100 and standard deviation 10. Then freeze these random numbers.a. Calculate the mean and
Ford is going to produce a new vehicle, the Pioneer, and wants to determine the amount of annual capacity it should build. Ford’s goal is to maximize the profit from this vehicle over the next five
Repeat the previous problem, but make the correlation between the two inputs equal to –0.7. Explain how the results change.Data from Previous Problem:When you use @RISK’s correlation feature to
1. Assume that Pacific National Bank remains with human tellers only.a. For each time period in Table 13.4, deter-mine the minimum number of tellers needed on station to service the customer
You can easily generate random numbers in a spread-sheet that have an exponential distribution with a given mean. For example, to generate 200 such numbers from an exponential distribution with λ =
A fast-food restaurant has one drive-through window. On average, 40 customers arrive per hour at the window. It takes an average of one minute to serve a customer. Assume that inter-arrival and
The MM1 Template.xlsx file is now set up so that you can enter any integer in cell E11 and the corresponding probability of that many in the system appears in cell F11. Change this setup so that
For an M/M/1 queueing system, L = λ/(µ – λ). Suppose that land µare both doubled. How does L change? How does W change? How does WQ change? How does LQ change? (Remember the basic queueing
Each airline passenger and his luggage must be checked to determine whether he is carrying weapons onto the airplane. Suppose that at Gotham City Airport, 2.6 passengers per minute arrive, on
A service facility consists of one server who can serve an average of two customers per hour (service times are exponential). An average of three customers per hour arrive at the facility
On average, 40 cars per hour are tempted to use the drive-through window at the Hot Dog King Restaurant. (We assume that inter-arrival times are exponentially distributed.) If a total of more than
A laundromat has five washing machines. A typical machine breaks down once every five days. A repairman can repair a machine in an average of 2.5 days. Currently, three repairmen are on duty. The
Referring to Problem 18, suppose the airline wants to determine how many checkpoints to operate to minimize operating costs and delay costs over a 10-year period. Assume that the cost of delaying a
Consider the following two queueing systems.■ System 1: An M/M/1 system with arrival rate λ and service rate 3µ.■ System 2: An M/M/3 system with arrival rate λ and each server working at rate
The Smalltown Credit Union experiences its greatest congestion on paydays from 11:30 A.M. until 1:00 P.M. During these rush periods, customers arrive according to a Poisson process at rate 2.1 per
Given the model in the Multi-server Simulation.xlsm file, what unit cost parameters should be used if we are interested in “optimizing” the system? Choose representative inputs and unit costs,
A telephone-order sales company must determine how many telephone operators are needed to staff the phones during the 9-to-5 shift. It is estimated that an average of 480 calls are received during
A company’s warehouse can store up to four units of a good. Each month, an average of 10 orders for the good are received. The times between the receipts of successive orders are exponentially
A printing shop receives an average of one order per day. The average length of time required to complete an order is half a day. At any given time, the print shop can work on at most one job.
The file P14_02.xlsx contains five years of monthly data on sales (number of units sold) for a particular company. The company suspects that except for random noise, its sales are growing by a
1. Determine whether you can develop a more accurate estimate of overhead costs.2. Wagner is now preparing a bid for an important order that may involve a considerable amount of repeat business. The
The file P14_03.xlsx contains monthly data on production levels and production costs during a four-year period for a company that produces a single product. Use simple regression on all of the data
Management of a home appliance store wants to understand the growth pattern of the monthly sales of a new technology device over the past two years. The managers have recorded the relevant data in
Do the sales prices of houses in a given community vary systematically with their sizes (as measured in square feet)? Answer this question by estimating a simple regression equation where the sales
The file P14_07.xlsx contains monthly values of the U.S. national debt (in dollars) from 1993 to early 2010. Fit an exponential growth curve to these data. Write a short report to summarize your
The management of a technology company is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees; see the file P14_08.xlsx.
We have discussed linear and exponential trend lines. Another popular choice is a power trend line, also called a constant elasticity trend line. This trend line has the form y = axb, and it has the
Sometimes curvature in a scatter plot can be fit adequately (especially to the naked eye) by several trend lines. We discussed the exponential trend line, and the power trend line is discussed in the
Suppose you are an analyst for a company that produces four products, and you are trying to decide how much of each product to produce next month. To model this decision problem, you need the unit
A trucking company wants to predict the yearly maintenance expense (Y) for a truck using the number of miles driven during the year (X1) and the age of the truck (X2, in years) at the beginning of
An antique collector believes that the price received for a particular item increases with its age and with the number of bidders. The file P14_14.xlsx contains data on these three variables for 32
Stock market analysts are continually looking for reliable predictors of stock prices. Consider the problem of modeling the price per share of electric utility stocks (Y). Two variables thought to
Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities:
The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file
The file P14_19.xlsxcontains the weekly sales of a particular brand of paper towels at a supermarket for a one-year period.a. Using a span of 3, forecast the sales of this product for the next 10
You have been assigned to forecast the number of aircraft engines ordered each month by Commins Engine Company. At the end of February, the forecast is that 100 engines will be ordered during April.
Simple exponential smoothing with α = 0.3 is being used to forecast sales of digital cameras at Lowland Appliance. Forecasts are made on a monthly basis. After August camera sales are observed, the
A version of simple exponential smoothing can be used to predict the outcome of sporting events. To illustrate, consider pro football. We first assume that all games are played on a neutral field.
Management of a home appliance store would like to understand the growth pattern of the monthly sales of Blu-ray disc players over the past two years. Managers have recorded the relevant data in the
A small computer chip manufacturer wants to forecast monthly ozperating costs as a function of the number of units produced during a month. The company has collected the 16 months of data in the
The file P14_35.xlsx contains the amount of money spent advertising a product (in thousands of dollars) and the number of units sold (in millions) for eight months.a. Assume that the only factor
When potential workers apply for a job that requires extensive manual assembly of small intricate parts, they are initially given three different tests to measure their manual dexterity. The ones who
Callaway Golf is trying to determine how the price of a set of clubs affects the demand for clubs. The file P14_37.xlsx contains the price of a set of clubs (in dollars) and the monthly sales
The file P14_38.xlsx lists the average salary for each Major League Baseball team from 2004 to 2009, along with the number of team wins in each of these years.a. Rearrange the data so that there are
GMC wants to decide whether to retool the Lyra and Libra plants. In addition, GMC wants to determine its production plan at each plant in the coming year. Based on the previous data, formulate a MILP
During 2001, many European markets for mobile phones reached saturation. Because of this, mobile phone operators started to shift their focus from growth and market share to cut-ting costs. One way
1. Using the spreadsheet model from Case 2.1 as a starting point, use Solver to find the optimal set of projects to approve. The solution should maximize the total NPV from the approved projects, and

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