Practical Management Science, Revised 3rd Edition Wayne L Winston, S. Christian Albright - Solutions

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Drug 1 sells for$6 per ounce, and drug 2 sells for $4 per ounce.Chemicals 1 and 2 can be produced by one of two production processes. Running process 1 for an hour requires 7 ounces of raw material and 2 hours skilled labor, and it yields 3 ounces of each chemical. Running process 2 for an hour
Capsule Drugs manufactures two drugs. The drugs are produced by blending two chemicals. By weight, drug 1 must contain at least 65% chemical 1, and drug 2 must contain at least 55% chemical
During the next four quarters, Dorian Auto must meet(on time) the following demands for cars: 4000 in quarter 1; 2000 in quarter 2; 5000 in quarter 3;1000 in quarter
What is the minimum number of trainees that need to be hired during months 1 to 8?(Note: Trainees must be integers. Experienced workers will probably end up being fractional. You have two options. First, you can ignore the fractional values. Second, you can use the ROUND function to round them to
AdminaStar processes Medicare claims. At the beginning of month 1 they have a backlog of 40,000 difficult claims and 60,000 easy claims. The predicted claim volume for months 1 through 8 is listed in the file P04_85.xlsx. At the beginning of month 1, AdminaStar has 70 experienced claim processors.
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 time so that it will be easier for the borrower to meet all payments. Suppose you borrow $60,000 on a
MusicTech manufactures and sells a portable music device called an mTune (similar to an iPod). At beginning of month 1, the company has $100,000 and 15 employees. Each machine the company owns has the capacity to make up to 900 mTunes per month, and each worker can make up to 600 mTunes per month.
The HiTech company produces Blu-Ray disc players.Estimated demands for the next four quarters are 5000, 10,000, 8000, and 2000. At the beginning of quarter 1, HiTech has 60 workers. It costs $2000 to hire a worker and $4000 to fire a worker. Workers are paid $10,000 per quarter plus $80 for each
Other relevant information is as follows:■ Workers are paid $5000 per month.■ It costs $500 to hold a car in inventory for a month.The holding cost is based on each month’s ending inventory.■ It costs $4000 to hire a worker.■ It costs $6000 to fire a worker.■ Each worker can make up to
An automobile manufacturer needs to plan its production for the next year. Demands for the next 12 months are forecasted to be 940, 790, 360, 720, 270, 130, 160, 300, 990, 290, 280, and
On line 1, 1300 hours of time are available, and 500 hours are available on line
A company produces two products: A and B. Product A sells for $11 per unit and product B sells for$23 per unit. Producing a unit of product A requires two hours on assembly line 1 and one unit of raw material.Producing a unit of product B requires two units of raw material, one unit of A, and two
Determine how United Steel can minimize the cost of manufacturing the desired steel.
United Steel manufactures two types of steel at three different steel mills. During a given month, each steel mill has 200 hours of blast furnace time available.Because of differences in the furnaces at each mill, the time and cost to produce a ton of steel differ for each mill, as listed in the
Assuming that he can put no more than$50,000 in any investment, develop an LP model to help the investor achieve his goal.
In addition to these investments, the investor can invest as much money each year as he wants in CDs, which pay 3% interest.The investor wants to maximize his available cash in year
An investor has $100,000 to invest right now (the beginning of year 1). The cash flows associated with five available investments are listed in the file P04_61.xlsx. For example, every dollar invested in A in year 1 yields $1.40 in year
Up to 50,000 ounces of drug 1 can be sold at $30 per ounce; up to 60,000 ounces of drug 2 can be sold at $25 per ounce. Up to 45,000 ounces of chemical 1 can be purchased at $15 per ounce, and up to 55,000 ounces of chemical 2 can be purchased at$18 per ounce. Determine how to maximize the
A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be at least 70%chemical 1, and drug 2 must be at least 60%chemical
It takes a shoemaker 20 minutes to produce a pair of shoes. Each shoemaker works 150 hours per month plus up to 40 hours per month of overtime.A shoemaker is paid a regular salary of $2000 per month plus $20 per hour for overtime. At the beginning of each month, Shoemakers can either hire or fire
Shoemakers of America forecasts the following demand for the next six months: 5000 pairs in month 1; 6000 pairs in month 2; 7000 pairs in month 3; 9000 pairs in month 4; 6000 pairs in month 5; 5000 pairs in month
A bus company believes that it will need the following numbers of bus drivers during each of the next five years: 60 drivers in year 1; 70 drivers in year 2;50 drivers in year 3; 65 drivers in year 4; 75 drivers in year
In the pension fund model, if the amount of money initially is less than the amount found by Solver, then James will not be able to meet all of the pension fund payments. Use the current model to demonstrate that this is true. To do so, enter a value less than the optimal value into cell B16. Then
Does the current model easily accommodate such investments? Try it with some cash outlay data you make up, run Solver, and interpret the results.
Suppose the investments in the Barney-Jones model sometimes require cash outlays in more than one year. For example, a $1 investment in investment B might require $0.25 to be spent in year 1 and$0.75 to be spent in year
James decides he would like to break these out into several rows of calculations: Beginning cash (for 2010, this is the amount allocated; for other years, it is the unused cash, plus interest, from the previous year), Amount spent on bonds (positive in 2010 only), Amount received from bonds
In the pension fund model, suppose James has been asked to see how the optimal solution will change if the required payments in years 2015 to 2024 all increase by the same percentage, where this percentage could be anywhere from 5% to 25%. Use an appropriate one-way SolverTable to help him out, and
Its unit cost in 2010 is $1020, it returns coupons of $70 in years 2011 to 2014 and a payment of $1070 in 2015. Modify the model to incorporate this extra bond and reoptimize. Does the solution change—that is, should James purchase any of bond 4?
In the pension fund model, suppose there is a fourth bond, bond
In the pension fund model, suppose there is an upper limit of 60 on the number of bonds of any particular type that can be purchased. Modify the model to incorporate this extra constraint and then reoptimize.How much more money does James need to allocate initially?
In the Barney-Jones investment model, we ran investments across columns and years down rows. Many financial analysts seem to prefer the opposite. Modify the spreadsheet model so that years go across columns and investments go down rows. Run Solver to ensure that your modified model is correct.
Modify the Barney-Jones investment model so that a minimum amount must be put into any investment, although this minimum can vary by investment. For example, the minimum amount for investment A might be $0, whereas the minimum amount for investment D might be $50,000. These minimum amounts should
In the Barney-Jones investment model, increase the maximum amount allowed in any investment to$150,000. Then run a one-way sensitivity analysis to the money market rate on cash. Capture one output variable: the maximum amount of cash ever put in the money market. You can choose any reasonable range
In the current blending model, a barrel of any input results in a barrel of output. However, in a real blending problem, there can be losses. Suppose a barrel of input results in only a fraction of a barrel of output. Specifically, each barrel of either crude oil used for gasoline results in only
Suppose SureStep could begin a machinery upgrade and training program to increase its worker productivity. This program would result in the following values of labor hours per pair of shoes over the next four months: 4, 3.9, 3.8, and 3.8. How much would this new program be worth to SureStep, at
The current solution to SureStep’s no-backlogging aggregate planning model requires a lot of firing.Run a one-way SolverTable with the firing cost as the input variable and the numbers fired as the outputs.Let the firing cost increase from its current value to double that value in increments of
SureStep is currently getting 160 regular-time hours from each worker per month. This is actually calculated from 8 hours per day times 20 days per month. For this, they are paid $9.375 per hour(1500160). Suppose workers can change their contract so that they only have to work 7.5 hours per day
In the post office example, suppose that each full-time employee works eight hours per day. Thus, Monday’s requirement of 17 workers can be viewed as a requirement of 8(17) 136 hours. The post office can meet its daily labor requirements by using both full-time and part-time employees. During
Why is it generally necessary to add nonnegativity constraints to an optimization model? Wouldn’t Solver automatically choose nonnegative values for the changing cells?
A company manufactures two products on two machines. The number of hours of machine time and labor depends on the machine and product as shown in the file P03_43.xlsx. The cost of producing a unit of each product depends on which machine produces it.These unit costs also appear in the same file.
It has 500 hours per week of machine time at Indianapolis and 400 hours per week at Los Angeles.a. Determine how the company can minimize the cost of producing the required drugs.b. Use SolverTable to determine how much the company would be willing to pay to purchase a combination of A extra hours
A pharmaceutical company manufactures two drugs at Los Angeles and Indianapolis. The cost of manufacturing a pound of each drug depends on the location, as indicated in the file P03_42.xlsx.The machine time (in hours) required to produce a pound of each drug at each city is also shown in this
(You can assume that a given worker gets the same quarter off during each year.)b. Suppose the company can pay a flat fee for a training program that increases the productivity of all of its workers. Use SolverTable to see how much the company would be willing to pay for a training program that
Each year, a shoe manufacturing company faces demands (which must be met on time) for pairs of shoes as shown in the file P03_40.xlsx. Employees work three consecutive quarters and then receive one quarter off. For example, a worker might work during quarters 3 and 4 of one year and quarter 1 of
A company that builds sailboats wants to determine how many sailboats to build during each of the next four quarters. The demand during each of the next four quarters is as follows: first quarter, 160 sailboats;second quarter, 240 sailboats; third quarter, 300 sailboats; fourth quarter, 100
A company manufactures two types of trucks. Each truck must go through the painting shop and the assembly shop. If the painting shop were completely devoted to painting type 1 trucks, 800 per day could be painted, whereas if the painting shop were completely devoted to painting type 2 trucks, 700
Maggie Stewart loves desserts, but due to weight and cholesterol concerns, she has decided that she must plan her desserts carefully. There are two possible desserts she is considering: snack bars and ice cream.After reading the nutrition labels on the snack bar and ice cream packages, she learns
A company faces the following demands during the next three weeks: week 1, 2000 units; week 2, 1000 units; week 3, 1500 units. The unit production costs during each week are as follows: week 1, $130; week 2, $140; week 3, $150. A holding cost of $20 per unit is assessed against each week’s ending
As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the
Some analysts complain that spreadsheet models are difficult to resize. You can be the judge of this.Suppose the current product mix problem is changed so that there is an extra resource, packaging labor hours, and two additional PC models, 9 and 10.What additional input data are required? What
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 product mix.Skill-Extending Problems
Modify PC Tech’s product mix model so that there is no maximum sales constraint. (This is easy to do in the Solver dialog box. Just highlight the constraint and click on the Delete button.) Does this make the problem unbounded? Does it change the optimal solution at all? Explain its effect.
Using the graphical solution of the product mix model as a guide, suppose there are only 2800 testing hours available. How do the answers to the previous problem change? (Is the previous solution still optimal? Is it still feasible?)
There are five corner points in the feasible region for the product mix problem. We identified the coordinates of one of them: (560, 1200). Identify the coordinates of the others.a. Only one of these other corner points has positive values for both changing cells. Discuss the changes in the selling
If all of the inputs in PC Tech’s product mix problem are nonnegative (as they should be for any realistic version of the problem), are there any input values such that the resulting model has no feasible solutions? (Refer to the graphical solution.)
The file P02_43.xlsx contains a template for a car loan. Specifically, once values are entered in the blue cells, you need to enter formulas in the gray cells to calculate the amount financed, the monthly payment(assuming that monthly payments stay the same throughout the term of the loan), 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 assumptions on project growth impact payback. Suppose, for example, that a project requires a $300
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 of 40%.
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 the following series: a payment of $25,000 today(assumed to be June 15, 2010), and cash inflows
The idea is that if the discount rate is greater than the IRR, the company will not pursue the project, but if the discount rate is less than the IRR, the project is financially attractive.a. Use Excel’s Goal Seek tool to find the IRR for the Acron model.b. Excel also has an IRR function. Look it
Is this percentage change constant? When expressed as a decimal, what number is it very close to? Write a brief memo on what you have learned about exponential curves from these calculations.Skill-Extending Problem 13.In the profit model in this section, we used the power curve to relate demand and
For each of these values of x, find the percentage change in y when x increases by one unit.That is, find the percentage change in y when x increases from 5 to 6; when it increases from 10 to 11;and when it increases from 20 to
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 increments of 500, and allow the unit expediting cost to vary from$36 to $45 in increments of $1.
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. Sometimes the quantity discount structure is such that the unit cost for the first so many items 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 use the new range name. Modify the formula so that it does. Then click on cell G4 and paste the new
The Sales2 variable in the file from the previous problem was created from the Sales1 variable by multiplying by monthly seasonal factors. Basically, the summer months are high and the winter months are low.This might represent the sales of a product that has a linear trend and seasonality.a.
The file P16_62.xlsx contains five years of monthly data for a company. The first variable is Time (1–60).The second variable, Sales1, has data on sales of a product. Note that Sales1 increases linearly throughout the period, with only a minor amount of noise. (The third variable, Sales2, will be
The file P16_61.xlsx contains data on a motel chain’s revenue and advertising.a. Use these data and multiple regression to make predictions of the motel chain’s revenues during the next four quarters. Assume that advertising during each of the next four quarters is $50,000.(Hint: Try using
Pernavik Dairy produces and sells a wide range of dairy products. Because a government regulatory board sets most of the dairy’s costs and prices, most of the competition between the dairy and its competitors takes place through advertising. The controller of Pernavik has developed the sales and
You are trying to determine the effects of three packaging displays (A, B, and C) on sales of toothpaste.The file P16_59.xlsx contains the number of cases of toothpaste sold for nine consecutive weeks. The type of store (GR grocery, DI discount, and DE department store) and the store location
Confederate Express is attempting to determine how its monthly shipping costs depend on the number of units shipped during a month. The file P16_58.xlsx contains the number of units shipped and total shipping costs for the past 15 months.a. Use regression to determine a relationship between units
The file P16_57.xlsx contains data on the price of new and used Taurus sedans. All used prices are from 1995.For example, a new Taurus bought in 1985 cost$11,790, and the wholesale used price of that car in 1995 was $1700. A new Taurus bought in 1994 cost$18,680, and it could be sold used in 1995
(Based on an actual court case in Philadelphia.) In the 1994 congressional election, the Republican candidate outpolled the Democratic candidate by 400 votes (excluding absentee ballots). The Democratic candidate outpolled the Republican candidate by 500 absentee votes. The Republican candidate
The auditor of Kaefer Manufacturing uses regression analysis during the analytical review stage of the firm’s annual audit. The regression analysis attempts to uncover relationships that exist between various account balances. Any such relationship is subsequently used as a preliminary test of
The belief that larger majorities for an incumbent president in a presidential election help the incumbent’s party increase its representation in the House and Senate is called the coattail effect. The file P16_54.xlsx gives the percent by which each president since 1948 won the election and the
The file P16_53.xlsx contains data on pork sales. Price is in dollars per hundred pounds, quantity sold is in billions of pounds, per capita income is in dollars, U.S. population is in millions, and GNP is in billions of dollars.a. Use the data on all potential explanatory variables to develop a
The auditor of Kiely Manufacturing is concerned about the number and magnitude of year-end adjustments that are made annually when the financial statements of Kiely Manufacturing are prepared. Specifically, the auditor suspects that the management of Kiely Manufacturing is using discretionary
The file P16_51.xlsx contains data on monthly U.S.housing sales (in thousands of houses).a. Use Winters’ method with 0.1 and 0.3 to forecast this series. Ask for 12 months of future forecasts. Then use Winters’ method a second time with the values of the smoothing constants that
Let Yt be the sales during month t (in thousands of dollars)for a photography studio, and let Pt be the price charged for portraits during month t. The data are in the file P16_50.xlsx.a. Use regression to fit the following model to these data: Yt a b1Pt b2Yt1. This says that current sales
The file P16_49.xlsx contains quarterly revenues of Toys “R” Us. Discuss the seasonal and trend components of the growth of Toys “R” Us revenues. Also, use any reasonable forecasting method to forecast quarterly revenues for the next year. Explain your choice of forecasting method.
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 are hired are then periodically given a performance rating on a 0 to 100 scale that combines their
Callaway Golf is trying to determine how the price of a set of clubs affects the demand for clubs. The file P16_47.xlsx contains the price of a set of clubs (in dollars)and the monthly sales (in millions of sets sold).a. Assume the only factor influencing monthly sales is price. Fit the following
The file P16_46.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 influencing monthly sales is advertising. Fit the following two curves to these data: linear (Y a bX)
The beta of a stock is found by running a regression with the monthly return on a market index as the explanatory variable and the monthly return on the stock as the dependent variable. The beta of the stock is then the slope of this regression equation.a. Explain why most stocks have a positive
Management of a home appliance store in Charlotte wants to understand the growth pattern of the monthly sales of DVD units over the past 2 years. Managers have recorded the relevant data in the file P16_44.xlsx.The question is whether the sales of DVD units have been growing linearly over the past
The file P16_43.xlsx contains the sales in (millions of dollars) for Procter and Gamble.a. Use these data to predict Procter & Gamble sales for the next two years. You need consider only a linear and exponential trend, but you should justify the equation you choose.b. Use your part a answer to
The file P16_42.xlsx contains the sales (in millions of dollars) for Sun Microsystems.a. Use these data to predict the company’s sales for the next two years. You need consider only a linear and exponential trend, but you should justify the equation you choose.b. In words, how do your predictions
The file P16_41.xlsx lists sales (in millions of dollars)of Dell Computer during the period from 1987 to 1997(where year 1 corresponds to 1987).a. Fit an exponential trendline to these data.b. Use your part a answer to predict 1999 sales for Dell.c. Use your part a answer to describe how the sales
At the end of month 13, what is the forecast for month 14? For month 15? Assume 0.2.
Holt’s method assumes an additive trend. For example, a trend of 5 means that the level will increase by 5 units per period. Suppose there is actually a multiplicative trend. This means that if the current estimate of the level is 50, and the current estimate of the trend is 1.2, we would predict
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. Before each day of play, we assume that each team has a rating. For example, if the rating for the
The file P16_38.xlsx contains monthly time series data for total U.S. retail sales of building materials (which includes retail sales of building materials, hardware and garden supply stores, and mobile home dealers).a. Is seasonality present in these data? If so, characterize the seasonality
The file P16_37.xlsx contains monthly retail sales of U.S. liquor stores.a. Is seasonality present in these data? If so, characterize the seasonality pattern.b. Use Winters’ method to forecast this series with smoothing constants 0.1 and 0.3.Does the forecast series seem to track the
The University Credit Union is open Monday through Saturday. Winters’ method is being used to predict the number of customers entering the bank each day. (The six days of the week are considered the “seasons.”)After observing the number of arrivals on Monday, the updated estimates of level
Consider the American Express closing price data from Problem 22 in the file P16_22.xlsx.a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model? Why?b. Use Holt’s exponential smoothing to
TOD Chevy is using Holt’s method to forecast weekly car sales. Currently, the level of the series is estimated to be 50 cars per week, and the trend is estimated to be 6 cars per week. During the current week, 30 cars are sold. After observing the current week’s sales, forecast the number of
The file P16_33.xlsx contains weekly data for the S&P 500 stock index from the beginning of 2002 to mid-2003. (It was downloaded from the Yahoo! site. You can follow the hyperlink in the file to obtain more recent data if you like.) In particular, the file lists closing prices in column H, adjusted
The file P16_32.xlsx contains yearly data on the proportion of Americans under the age of 18 living below the poverty level.a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model? Why?b. Use
The file P16_31.xlsx contains the monthly number of airline tickets sold by the CareFree Travel Agency.a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model? Why?b. Use simple exponential
The file P16_30.xlsx contains the quarterly numbers of applications for home mortgage loans at a branch office of Northern Central Bank.a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model?

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Practical Management Science, Revised 3rd Edition Wayne L Winston, S. Christian Albright - Solutions

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