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practical management science
Questions and Answers of
Practical Management Science
The quantity discount model in Example 12.2 uses one of two possible types of discount structures. It assumes that if the company orders 100 units, say, each unit costs $150. This provides a big
In Example 12.3, SolverTable was used to show what happens when the unit shortage cost varies. As the table indicates, the company orders more and allows more backlogging as the unit shortage cost
In the basic EOQ model in Example 12.1, suppose that the fixed cost of ordering and the unit holding cost are both multiplied by the same factor f. (Remember that the unit holding cost is s + ic, so
The first (R,Q) model in this section assumes that the total shortage cost is proportional to the amount of demand that cannot be met from on-hand inventory. Similarly, the second model assumes that
Ford has four automobile plants. Each is capable of producing the Focus, Mustang, or Crown Victoria, but it can produce only one of these cars. The fixed cost of operating each plant for a year
In Example 7.1, two points on the demand curve were given (Figure 7.11).a. Suppose three additional points are estimated by Madison: (1) demand of 460 when price is $65, (2) demand of 355
In Example 7.1, one demand function is linear and the other is called a constant elasticity demand function. Using data tables, show that the price elasticity in the linear demand function is not
In the pricing model in Example 7.1 with the constant elasticity demand function, the assumption is that all units demanded are sold. Suppose the company has the capacity to produce only 200 units.
Continuing the previous problem, create a two-way data table similar to the one-way data table in Figure?7.11. This time, however, allow price to vary down a column and allow the capacity to vary
Continuing Problem 3 in a slightly different direction, create a two-way SolverTable where the inputs are the elasticity and the production capacity, and the outputs are the optimal price and the
In the exchange rate model in Example 7.2, suppose the company continues to manufacture its product in the United States, but now it sells its product in the United States, the United Kingdom, and
The preceding problem indicates how fewer alternatives can cause total cost to increase. This problem indicates the opposite. Starting with the solution to the advertising selection problem in
Change the exchange rate model in Example 7.2 slightly so that the company is now a UK manufacturing company producing for a U.S. market. Assume that the unit cost is now £75, the demand function
In the exchange rate model in Example 7.2, 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
In the complementary-product pricing model in Example 7.3, the elasticity of demand for suits is currently -2.5. Use SolverTable to see how the optimal price of suits and the optimal profit vary as
Continuing Problem 6, suppose the company is selling in the United States, the United Kingdom, and Japan. Assume the unit production cost is $50, and the exchange rates are 1.66 ($/£) and 0.00965
In the complementary-product pricing model in Example 7.3, we have assumed that the profit per unit from shirts and ties is given. Presumably this is because the prices of these products have already
Continuing the previous problem (the model in part a) one step further, assume that shirts and ties are also complementary. Specifically, assume that each time a shirt is purchased (and is not
In estimating the advertising response function in Example 7.5, we indicated that the sum of squared prediction errors or RMSE could be used as the objective, and we used RMSE. Try using the sum of
The best-fitting advertising response function in Example 7.5 fits the observed data. This is because we rigged the observed data to fall close to a curve of the form in Equation (7.4). See
The advertising response function in Equation (7.4) is only one of several non-linear functions that could be used to get the same “increasing at a decreasing rate” behavior in Example
By the time you are reading this, the 2013–2014 NBA season will have finished, and the results should be available at http://www.basketball-reference.com/leagues/NBA_2014_games.html. Do whatever it
The method for rating teams in Example 7.8 is based on actual and predicted point spreads. This method can be biased if some teams run up the score in a few games. An alternative possibility is to
In the model in Example 7.9, stock 2 is not in the optimal portfolio. Use SolverTable to see whether it ever enters the optimal portfolio as its correlations with stocks 1 and 3 vary. Specifically,
The stocks in Example 7.9 are all positively correlated. What happens when they are negatively correlated? Answer for each of the following scenarios. In each case, two of the three correlations are
In many cases, the portfolio return is at least approximately normally distributed. Then Excel’s NORMDIST function can be used to calculate the probability that the portfolio return is
Given the data in the file Stock Beta.xlsx, estimate the beta (and alpha) for Microsoft (MSFT). Do this for each criterion and each period of time to obtain a table analogous to that in the
Solve the previous problem, but analyze GE instead of Microsoft.Data from Previous Problem:Given the data in the file Stock Beta.xlsx, estimate the beta (and alpha) for Microsoft (MSFT). Do this
Suppose Ford currently sells 250,000 Ford Mustangs annually. The unit cost of a Mustang, including the delivery cost to a dealer, is $16,000. The current Mustang price is $20,000, and the current
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
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