Questions and Answers of Practical Management Science

In a production process model such as Repco’s, certain inputs make no sense in the usage table (the range B7:D9 of the model). For example, suppose that, in addition to current usages, each unit of
We claimed that the Repco model could either con-strain the units produced to be greater than or equal to the units used by production or constrain the units sold to be nonnegative. Modify the model
Suppose there is a fourth drug, drug D, that Repco can produce and sell. Each unit of drug D requires four labor hours, one unit of drug A, and one unit of drug C to produce, and it sells for $150
Run a one-way sensitivity analysis on the optimal solution to the unit selling price of drug A in the Repco model. If this price is high enough, will Repco start selling drug A in addition to
We warned you about clearing denominators in the quality constraints. This problem illustrates what can happen if you don’t do so.a. Implement the quality constraints as indicated in Inequality
In Chandler’s blending model, suppose a chemical ingredient called CI is needed by both gasoline and heating oil. At least 3% of every barrel of gasoline must be CI, and at least 5% of every barrel
How sensitive is the optimal solution (barrels of each input and output sold and total revenue) to the required quality levels? Answer this by running a two-way SolverTable with these five outputs.
Use SolverTable in Chandler’s blending model to see whether, by increasing the selling price of gasoline, you can get an optimal solution that produces only gasoline, no heating oil. Then use
In the current no-backlogging problem, Sure Step doesn’t hire any workers and uses almost no overtime. This is evidently because of low demand. Change the demands to 6000, 8000, 5000, and 3000, and
In the employee scheduling example, suppose that the company can require the employees to work one day of overtime each week on the day immediately following this five-day shift. For example, an
Suppose the company has 25 full-time employees and is not allowed to hire or fire any of them. Determine a schedule that maximizes the number of weekend days off received by these employees.
Suppose there are three objectives, not just two: the total advertising cost, the total number of excess exposures to men, and the total number of excess exposures to women. Continuing the approach
In the dual-objective advertising model, we put a budget constraint on the total advertising cost and then maximized the total number of excess exposures. Do it the opposite way, reversing the roles
Suppose that General Flakes decides that it shouldn’t place any more than 10 ads on any given show. Modify the (original) advertising model appropriately to incorporate this constraint, and then
Suppose, in addition to the shows already listed, General Flakes wants to open the possibility of purchasing ads on the “Good Morning America” show on ABC. Make up any reasonable input data you
1. Develop an LP model to determine whether there are any arbitrage opportunities with the spot currency rates given in the file. Note that an arbitrage opportunity could involve several currencies.
Suppose, as a matter of corporate policy, that General Flakes decides not to advertise on the Rachael Ray show. Modify the original advertising model appropriately and find the new optimal solution.
1. You should develop an Excel optimization model to find the optimal strategy. This strategy should specify the number of each type of ac-count (0-due, 1-due, 2-due, 3-due) that should receive
In addition to the constraints already in the (original) advertising model, suppose General Flakes also wants to obtain at least 180 million exposures to men and at least 160 million exposures to
1. Dave is not absolutely sure that the "side" constraint of at least as much gas A as gas B is necessary. What is this constraint costing the company? That is, how much more revenue could
A graduated payment mortgage (GPM) enables the borrower to have lower payments earlier in the mortgage and increased payments later on. The assumption is the borrower’s income will increase over
The Internal Revenue Service (IRS) has determined that during each of the next 12 months it will need the numbers of supercomputers given in the file P04_88.xlsx. To meet these requirements, the
You own a wheat warehouse with a capacity of 20,000 bushels. At the beginning of month 1, you have 6000 bushels of wheat. Each month, wheat can be bought and sold at the prices per bushel listed in
A furniture company manufactures tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 15,000 board feet of oak and 21,000 board feet of pine
George needs help to decide how many grapes to buy, how much money to spend on advertising, how many bottles of wine to sell, and how much profit he can expect to earn over the two-year period.
Shelby Shelving is a small company that manufactures two types of shelves for grocery stores. Model S is the standard model; model Lx is a heavy-duty version. Shelves are manufactured in three major
A textile company produces shirts and pants. Each shirt requires two square yards of cloth, and each pair of pants requires three square yards of cloth. During the next two months the following
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
Calculate the amount financed, the monthly payment (assuming that monthly payments stay the same throughout the term of the loan), the total interest paid, and an amortization schedule. For the
Continuing the previous problem, use Goal Seek for each value of number mailed (once for 80,000, once for 90,000, and so on). For each, find the response rate that allows the company to break even.
1. In the absence of cannibalization, the sales of existing eTech products are expected to produce year 1 net revenues of $10 million, and the fore-cast of the annual increase in net revenues is
In the Quality Sweaters model, the range E9:E11 does not have a range name. Open your completed Excel file and name this range Costs. Then look at the formula in cell E12. It does not automatically
As the Quality Sweaters problem is now modeled, if all inputs remain fixed except for the number mailed, profit will increase indefinitely as the number mailed increases. This hardly seems
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
The spreadsheet model for Sam’s Bookstore contains a two-way data table for profit versus order quantity and demand. Experiment with Excel’s chart types to create a chart that shows this
In the Sam’s Bookstore problem, the quantity discount structure is such that all the units ordered have the same unit cost. For example, if the order quantity is 2500, then each unit costs $22.25.
The current spreadsheet model essentially finds the expected profit in several steps. It first finds the profit in cell B19 for a fixed value of demand. Then it uses a data table to find the profit
Continuing Problem 5, create a two-way data table for expected profit with order quantity along the side and unit expediting cost along the top. Allow the order quantity to vary from 500 to 4500 in
Suppose you have an extra six months of data on demands and prices, in addition to the data in the example. These extra data points are (350, 84), (385, 72), (410, 67), (400, 62), (330, 92), and
Consider the power curve y = 10000x–2.35. Calculate y when x = 5; when x = 10; and when x = 20. For each of these values of x, find the percentage change in y when x increases by 1%. That is, find
Consider the exponential curve y = 1000e–0.014x. Calculate y when x = 5; when x = 10; and when x = 20. For each of these values of x, find the percentage change in y when x increases by one unit.
In the profit model in this section, we used the power curve to relate demand and price because it has the lowest MAPE (as well as the lowest RMSE and MAE). However, the exponential curve was not far
Modify Acron’s model so that development lasts for an extra year. Specifically, assume that development costs of $7.2 million and $2.1 million are incurred at the beginnings of years 1 and 2, and
Modify Acron’s model so that sales increase, then stay steady, and finally decrease. Specifically, assume that the gross margin is $1.2 million in year 1, then increases by 10% annually through
Create a one-way data table in the Acron model to see how the NPV varies with discount rate, which is allowed to vary from 8% to 18% in increments of 0.5%. Explain intuitively why the results go in
The NPV function automatically discounts each of the cash flows and sums the discounted values. Verify that it does this correctly for Acron’s model by calculating the NPV the long way. That is,
In a situation such as Acron’s, where a one-time cost is followed by a sequence of cash flows, the internal rate of return(IRR) is the discount rate that makes the NPV equal to 0. The idea is that
The XNPV function can calculate NPV for any (possibly irregular) series of cash flows. Look this function up in Excel’s online help. Then use it to develop a spreadsheet model that finds the NPV of
Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand is $50.00. Her best guess is that she can sell 300 cups per week at $0.50 per cup. The variable cost
You are thinking of opening a Broadway play, I Love You, You’re Mediocre, Now Get Better! It will cost $5 million to develop the show. There are 8 shows per week, and you project the show will run
You are thinking of opening a small copy shop. It costs $5000 to rent a copier for a year, and it costs $0.03 per copy to operate the copier. Other fixed costs of running the store will amount to
Georgia McBeal is trying to save for her retirement. She believes she can earn 10% on average each year on her retirement fund. Assume that at the beginning of each of the next 40 years, Georgia will
A European call option on a stock earns the owner an amount equal to the price at expiration minus the exercise price, if the price of the stock on which the call is written exceeds the exercise
Repeat parts a – d of the previous problem for a six-month European put option with exercise price $40. Again, assume a current stock price of $35, a risk-free rate of 5%, and an annual volatility
The file P02_26.xlsx lists sales (in millions of dollars) of Dell Computer during the period 1987–1997 (where year 1 corresponds to 1987).a. Fit a power and an exponential trend curve to these
Dataware is trying to determine whether to give a $10 rebate, cut the price $6, or have no price change on a software product. Currently, 40,000 units of the product are sold each week for $45
The file P02_28.xlsx gives the annual sales for Microsoft (in millions of dollars) for the years 1984 – 1993, where 1984 = year 1.a. Fit an exponential curve to these data.b. Assuming you are back
Assume that the number of units sold of a product is given by 100 – 0.5 P + 26√A, where P is the price (in dollars) charged for the product and A is the amount spent on advertising (in thousands
A company manufacturers a product in the United States and sells it in England. The unit cost of manufacturing is $50. The current exchange rate (dollars per pound) is 1.51. The demand function,
The yield of a chemical reaction is defined as the ratio (expressed as a percentage) of usable output to the amount of raw material input. Suppose the yield of a chemical reaction depends on the
A bond is currently selling for $1040. It pays the amounts listed in the file P02_32.xlsx at the ends of the next six years. The yield of the bond is the interest rate that would make the NPV of the
Assume the demand for a company’s drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year,
Consider a project with the following cash flows: year 1, – $400; year 2, $200; year 3, $600; year 4, – $900; year 5, $1000; year 6, $250; year 7, $230. Assume a discount rate of 15% per year.a.
A software company is considering translating its program into French. Each unit of the program sells for $50 and incurs a variable cost of $10 to produce. Currently, the size of the market for the
The payback of a project is the number of years it takes before the project’s total cash flow is positive. Payback ignores the time value of money. It is interesting, however, to see how differing
You are entering the widget business. It costs $500,000, payable in year 1, to develop a prototype. This cost can be depreciated on a straight-line basis during years 1–5. Each widget sells for $40
Suppose you are borrowing $25,000 and making monthly payments with 1% interest. Show that the monthly payments should equal $556.11. The key relationships are that for any month t(Ending month t
You are thinking of starting Peaco, which will produce Peak babies, a product that competes with Ty’s Beanie Babies. In year 0 (right now), you will incur costs of $4 million to build a plant. In
Suppose the demand (in thousands) for a toaster is given by 100p–2, where p is the price in dollars charged for the toaster.a. If the variable cost of producing a toaster is $10, what price
The file P02_41.xlsx contains the cumulative number of bits (in trillions) of DRAM (a type of computer memory) produced and the price per bit (in thousandths of a cent).a. Fit a power curve that can
The IRR is the discount rate r that makes a project have an NPV of $0. You can find IRR in Excel with the built-in IRR function, using the syntax = IRR(range of cash flows). However, it can be
A project does not necessarily have a unique IRR. (Refer to the previous problem for more information on IRR.) Show that a project with the following cash flows has two IRRs: year 1, – $20; year 2,
The file P02_46.xlsx contains data on prices of products for several of a chain store’s locations, a discount schedule offered to customers depending on how much they spend, and commission rates of
1. The model should list the given financial information for all potential projects.2. The model should associate with each proposed project a cell that is 1 if the project is approved and 0 if it is
Discuss how the aggregate planning model could be extended to handle a company that produces several products on several types of machines. What information would you need to model this type of
Can you ever use the material in this chapter to help you make your own real-life decisions? Consider the following. You are about to take an important and difficult exam in one of your MBA courses,
The file P08_15.xlsx contains the following information about the top 25 MBA programs (according to the 1997 Business Week Guide): percentage of applicants accepted, percentage of accepted applicants
For the data in the file P08_17.xlsx, develop a classification rule to classify students as admits or non-admits.
For data in the file P08_16.xlsx, develop a rule to predict whether a person is likely to purchase your lasagna product. What variables appear to be the most useful?
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
Sales of a product over time often follow an S-shaped curve. Two functions that yield S-shaped curves are the Pearl (or logistic) curveand the Gompertz curveY = Leâ€“beâ€“ktHere, Y is
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 iswhere Y is the adoption level, L is an (unknown) upper
The file P08_10.xlsx 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 (8.1) that can be
You are given the following information concerning how a change in sales force effort impacts sales:a. A 50% cut in sales force effort reduces sales to 48% of its current value.b. Sales force effort
In the lawn mower production problem in Example 8.4, experiment with the penalty cost for unsatisfied pick-ups in week 1. If this cost is sufficiently small, does the company ever produce fewer than
In the lawn mower production problem in Example 8.4, 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
In the truck-loading problem in Example 8.3, we assumed that any product could be loaded into any compartment. Suppose the following are not allowed: pro duct 1 in compartment 2, product 2 in
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. It also shows how much members of each group are willing to
In Example 8.2, determine the optimal pricing policy if Menthos are sold in only a one-pack or a six-pack.
In Example 8.2, determine the best pricing policy if quantity discounts with a single-price breakpoint are used.
This is an extension of Case 2.1 from Chapter 2, so you should read that case first. It asks you to develop a spreadsheet model, using a 0-1 variable for each potential project, so that Cliff Erland,
Modify the function in Example 8.1 so that it becomes f(x) = x sin(x) for 0 ≤ x ≤ 30. Plot a lot of points from 0 to 30 to see what the graph of this function looks like. Then use GRG Nonlinear
The MBA program at State University has approximately 260 incoming students each fall semester. These students are divided into cohorts of approximately 65 students each, and the students in each
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
The file P08_30.xlsx contains quarterly revenue for Nike for the years 1991 to 1998. It also contains quarterly “indicator” variables Q1, Q2, and Q3. Here Q1 is 1 for the first quarter of a
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
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 P08_32.xlsx. To be sold, each package must consist of at
During the next 12 months, the amounts of electric power needed (in thousands of kwh) are listed in the file P08_33.xlsx. This power can be supplied using four generators. The generating capacity (in
Ten data sets must be assigned for storage to one of three disk drives. Each disk drive can store 25 GB (about 25,000 MB). The sizes of the data sets (in MB) are listed in the file P08_35.xlsx. When
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

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