Practical Management Science 6th Edition Wayne L. Winston, Christian Albright - Solutions

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A farmer in Iowa owns 45 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields $200 profit, requires 3 workers, and requires 2 tons of fertilizer; each with corn yields $300 profit, requires 2 workers, and requires 4 tons of fertilizer.The farmer has
Furnco manufactures desks and chairs. Each desk uses 4 units of wood, and each chair uses 3 units of wood.A desk contributes $40 to profit, and a chair contributes$25. Marketing restrictions require that the number of chairs produced be at least twice the number of desks produced. There are 20
Running process 1 for an hour costs $4 and yields 3 units of A, 1 unit of B, and 1 unit of C. Running process 2 for an hour costs $1 and yields 1 unit of A and 1 unit of B. To meet customer demands, at least 10 units of A, 5 units of B, and 3 units of C must be produced daily.a. Use Solver to
Leary Chemical manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes: 1 and
How does this change the optimal production schedule? How does it change the optimal total cost?
Modify the Pigskin spreadsheet model so that demand in any of the first 5 months must be met no later than a month late, whereas demand in month 6 must be met on time. For example, the demand in month 3 can be met partly in month 3 and partly in month
How does this change the optimal production schedule? How does it change the optimal total cost?
Modify the Pigskin spreadsheet model so that except for month 6, demand need not be met on time. The only requirement is that all demand be met eventually by the end of month
In one modification of the Pigskin problem, the maximum storage constraint and the holding cost are based on the average inventory (not ending inventory) for a given month, where the average inventory is defined as the sum of beginning inventory and ending inventory, divided by 2, and beginning
As indicated by the algebraic model of the Pigskin problem, 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 current
Modify the Pigskin model so that there are 8 months in the planning horizon. You can make up reasonable values for any extra required data. Don’t forget to modify range names. Then modify the model again so that there are only 4 months in the planning horizon.Do either of these modifications
(These are in hundreds of footballs.) Keep track of the values in the changing cells and the target cell.
Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 100 in increments of
What additional data are required? What modifications are necessary in the spreadsheet model (including range name changes)?Make up values for any extra required data and incorporate these into a modified spreadsheet model. (You might want to try inserting new columns in the middle of your range,
Some analysts complain that spreadsheet models are difficult to resize. We’ll let you be the judge of this.Suppose the current product mix problem is changed so that there is an extra resource, plastic, and two additional frame types, 5 and
Suppose we want to increase all three of the resource availabilities in the product mix model simultaneously by the same factor. We want this factor to vary from 0.8 to 2.0 in increments of 0.1. For example, if this factor is 1.0, we get the current model, whereas if the factor is 2.0, the resource
In the current solution to the product mix model, type 4 frames are not produced at all. This is due, at least in part, to the low unit selling price of type 4 frames. Use SolverTable appropriately to determine how large this unit selling price would have to be before type 4 frames would be
Create a two-way SolverTable for the product mix model, where profit is the only output and the two inputs are the hourly cost of labor and the total labor hours available. Let the hourly cost of labor vary from$6 to $10 in increments of $1, and let the total labor hours vary from 3000 to 7000 in
Use SolverTable to run a sensitivity analysis on the cost per ounce of metal in the product mix model. Let this unit cost vary from $0.30 to $1.30 in increments of $0.20, and keep track of the values in the changing cells and the target cell. Discuss what happens to the optimal product mix. Also,
In the product mix model, it makes sense to change the maximum sales constraint to a “minimum sales”constraint, simply by changing the direction of the inequality. Then the input values in row 18 can be considered customer demand that must be met. Make this change and rerun Solver. What do you
Modify Monet’s product mix model so that there is no maximum sales constraint. (In the Solver dialog box, 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.
Consider the graphical solution to the dessert problem. Now imagine that another constraint—any constraint—is added. Which of the following three things are possible: (1) feasible region shrinks;(2) feasible region stays the same; (3) feasible region expands? Which of the following three things
You want calories per serving of snack bars to vary from 100 to 140 in increments of 5, and you want to keep track of the values in the changing cells and the target cell. Modify the model slightly so that this analysis can be performed with a one-way SolverTable.
The SolverTable add-in can be used for less obvious sensitivity analyses. Suppose in the dessert model that you want to vary both of the calories per serving values in row 5, but you want them to stay in the same ratio, 4 to
The graphical solution to the dessert problem indicates that the optimal solution contains both snack bars and ice cream because the slope of the total taste index line is between the slopes of the two constraint lines for calories and fat. With this in mind, consider changes in the taste index of
There are five corner points in the feasible region for the dessert problem. We identified the coordinates of one of them: (1.25, 1.875). Identify the coordinates of the others. If we vary the taste index values in row 12 of the spreadsheet model, is it possible for each of these corner points to
Use the graphical solution of Maggie’s dessert problem to determine all values of the right-hand side of the total daily gram requirement that make the model infeasible—that is, it has no feasible solutions.
Changing cells in the dessert model can be measured in servings or in grams. Modify the spreadsheet model so that they are measured in grams, and use Solver to find the optimal solution. Discuss how the solution to this modified model is different from the solution we found; discuss how they are
Continuing the previous problem, perform a sensitivity analysis on the taste index of the cookies. Let this index vary from 60 to 100 in increments of 5, and keep track of the values in the changing cells and the target cell. Discuss your findings.
Modify the spreadsheet model to include this new dessert, and use Solver to find the optimal dessert plan.
In Maggie’s dessert problem, assume there is another possible dessert, in addition to snack bars and ice cream, that Maggie can consider: oatmeal raisin cookies. Each cookie, which is considered a “serving,”weighs 43 grams, contains 140 calories, and contains 6 grams of fat. Maggie likes
Other sensitivity analyses besides those discussed could be performed on Maggie’s dessert model. Use SolverTable to perform each of the following. In each case, keep track of the values in the changing cells and the target cell, and discuss your findings.a. Let the fat per serving of snack bars
How could you use Goal Seek to find a project’s IRR?(Refer to Problem 44 for more information on IRR.)
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, $82; year 3,$60; year 4, $2. (Note: It can be shown that if the cash flow of a project changes sign
How could you determine a discount rate that makes two projects have the same NPV?
Suppose the demand (in thousands) for a toaster is given by 100p2, where p is the price in dollars charged for the toaster.a. If the variable cost of producing a toaster is $10, what price will maximize profit?b. The elasticity of demand is defined as the percentage change in demand created by a
What annual percentage growth rate g does Peaco require to “pay back” the plant cost by the end of year 5?
Unit sales are expected to grow by the same percentage (g)each year. During years 1 to 5, Peaco incurs two types of costs: variable costs and SG&A (selling, general, and administrative) costs. Each year, variable costs equal half of revenue. During year 1, SG&A costs equal 40% of revenue. This
You are thinking of starting Peaco, which will produce Peakbabies, 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 year 1, you expect to sell 80,000 Peakbabies for a unit price of $25. The price of$25 will remain
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. Compute the project’s NPV if cash flows occur at the ends of the respective years.b. Compute the
Assume the demand for the drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If you build a plant that can produce x units of Wozac per year, it will cost $16x. Each unit of Wozac is sold for $3. Each unit of Wozac produced incurs a variable production cost of
A bond is currently selling for $1040. It pays the amounts listed in the file P02_32.xlsx at the end of the next 6 years. The yield of the bond is the interest rate that would make the NPV of the bond’s payments equal to the bond’s price. Use Excel’s Goal Seek tool to find the yield of the
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 is found to depend on the length of time the process is run and the temperature at which the process is run. The yield
You are given the data on the price of new Taurus sedans and used Taurus sedans in the file P02_30.xlsx.All used prices are in amounts paid in 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
Assume that the number of units sold of a product is given by 100 0.5P 26A, where P is the price(in dollars) charged for product and A is the amount spent on advertising (in thousands of dollars). Each unit of the product costs $5 to produce. What combination of price and advertising will
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. By what percentage do you estimate that Microsoft will grow each year?c. Why can’t a high rate of exponential growth
The file P02_27.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 data. Which fits the data better?b. Use your part a answer to predict 1999 sales for Dell.c. Use your
Dataware is trying to determine whether to give a $10 rebate, to cut the price $6, or to have no price change on a software product. Currently, 40,000 units of the product are sold each week for $45. The variable cost of the product is $5. The most likely case appears to be that a $10 rebate will
Repeat parts a–d of the previous problem for a 6-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%.
You are thinking of opening a small copy shop. It costs $5000 to rent a copier for a year and costs $0.03 per copy to operate the copier. Other fixed costs of running the store will amount to $400 per month. You plan to charge an average of $0.10 per copy, and the store will be open 365 days per
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 set up a spreadsheet model that finds the NPV of the following series: a payment of $25,000 today(assumed to be June 15, 2006), and cash inflows
The idea is that if the discount rate is greater than the IRR, the company will not pursue the project; whereas 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.
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
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 direction they go—that is, the NPV decreases as the discount rate increases. Should Acron pursue
Perform a sensitivity analysis with a two-way data table to see how NPV varies with the length of the increase period (currently 6 years) and the length of the constant period (currently 4 years). Comment on whether Acron should pursue the drug, given your results.
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 year 6, then stays constant through year 10, and finally decreases by 5%annually through year
Again, calculate the NPV discounted back to the beginning of year 1, and perform the same sensitivity analyses. Comment on the effects of this change in timing.
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 then the sales in the current model occur one year later, that is, from year 2 until year
In the profit model in this section, we used the power curve to relate demand and price because it has the lowest MAPE. However, the exponential curve was not far behind. Rework the profit model using the exponential curve to relate demand to price. Write a brief memo indicating whether you get
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.
For each of these values of x, find the percentage change in y when x increases by 1 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
Consider the exponential curve y 1000e0.014x.Calculate y when x 5; when x 10; and when x
For each of these values of x, find the percentage change in y when x increases by 1%. That is, find the percentage change in y when x increases from 5 to 5.05; when it increases from 10 to 10.1; and when it increases from 20 to 20.2. Is this percentage change constant? What number is it very close
Consider the power curve y 10000x2.35. Calculate y when x 5; when x 10; and when x
Continuing Problem 6, 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.
Then insert a new row below row 11 that lists the probabilities of these demands. Next, in the rows below the Profit Model label, calculate the units sold, revenue, cost, and profit for each demand. For example, the quantities in column C will be for the second possible demand. Finally, use
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 for each of several demands, and finally it uses SUMPRODUCT to find the expected profit. Modify 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 information graphically in an intuitive format. (Choose the format you would choose to give a presentation
As the Great Threads 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 realistic—the company could become infinitely rich! Discuss realistic ways to modify the model so that this
The sensitivity analysis in the Great Threads example was on the response rate. Suppose now that the response rate is known to be 8%, and the company wants to perform a sensitivity analysis on the number mailed. After all, this is a variable under direct control of the company. Create a one-way
In the Great Threads 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 list
A cosmetics company has identified a set of activities that must be performed to bring a new product to market. The activities, their precedence relations, and time estimates to complete each activity (in days) are shown in the following table.
Refer to the previous question. Create a spreadsheet model to simulate the completion times for Koene’s move. Assume that activity times follow a triangular distribution and perform 500 replications on the model.a. Estimate the probability of each activity falling on the critical path. Which
Refer to the previous question. Create a spreadsheet model to simulate the completion times for servicing cars. Assume that activity times follow a triangular distribution, and perform 500 replications on the model.a. Estimate the probability of each activity falling on the critical path.b. On
Consider the following set of activities: a. Draw the CPM network for this problem.b. Identify each path through the network and its expected length.c. What is the critical path?d. Verify
Consider the following set of activities: a. Draw the CPM network for this problem.b. Manually determine the earliest and latest start and finish times for each activity and the
Refer to the data in the file on your data disk named QtrlySales.xls containing quarterly sales data for a Norwegian export company from 1993 through 2005. Prepare a line graph of these data. Do the data appear to be stationary or non stationary?
Prepare a line graph of these data. Do the data appear to be stationary or non-stationary?
Benjamin Franklin once said, “In this world nothing is certain but death and taxes.” Although that might be true, there is often great uncertainty involved in when one will encounter death and how much one must pay in taxes before arriving there. Another Benjamin made a very significant
Martin manufacturing company uses a piece of machinery that has three different bushings that periodically fail in service. The probability distribution of the life of each bushing is identical and is summarized by the following table.
Representatives from the American Heart Association are planning to go door-to-door throughout a community, soliciting contributions. From past experience, they know that when someone answers the door, 80% of the time it is a female and 20% of the time it is a male. They also know that 70% of the
Use regression analysis to answer the following questions.a. Fit a linear trend model to the data set. What is the estimated regression function?b. Interpret the R2 value for your model.c. Prepare a line graph comparing the linear trend predictions against the original data.d. What are the
Use regression analysis to answer the following questions.a. Fit a linear trend model to the data set. What is the estimated regression function?b. Interpret the R2 value for your model.c. Prepare a line graph comparing the linear trend predictions against the original data.d. What are the
Refer to the data in the file on your data disk named LaborForce.xls containing monthly data on the number of workers in the U.S. civilian labor force (in 1000s) from January 1998 through October 2005. Prepare a line graph of these data. Do the data appear to be stationary or nonstationary?
Refer to the data in the file on your data disk named CalfPrices.xls representing the selling price of three-month-old calves at a livestock auction during the past 22 weeks.Prepare a line graph of these data. Do the data appear to be stationary or nonstationary?
Use the multiplicative seasonal technique for stationary data to model the data. Use Solver to determine the optimal values of α and β.a. What are the optimal values of α and β?b. Prepare a line graph comparing the predictions from this method against the original data.c. What are the forecasts
Use Holt’s method to create a model that minimizes the MSE for the data set. Use Solver to determine the optimal values of α and β.a. What are the optimal values of α and β?b. Prepare a line graph comparing the predictions from Holt’s method versus the original data.c. What are the
Prepare a line graph of these data. Do the data appear to be stationary or nonstationary?
The Royalty Gold Corporation prospects for undiscovered gold deposits around the world. The company is currently investigating a possible site on the island of Milos off the coast of Greece in the Mediterranean. When prospecting, the company drills to collect soil and rock samples and then analyzes
This chapter noted that the R2 statistic cannot be relied upon as a goodness-of-fit measure in the regression approach to two-group DA. What was the value of the R2 statistic for the two-group DA example in this chapter? How does it compare with the percentage of correctly classified observations
Suppose that you are interested in creating a prediction interval for Y at a particular value of X1 (denoted by X1h ) using a simple linear regression model, and that data has not yet been collected. For a given sample size n, how you would attempt to collect the sample data to make the most
Show how R2a and Se are related algebraically (identify the function f(.) such that R2a = f(Se)).
Fidelity Savings & Loans (FS&L) operates several banking facilities throughout the Southeastern United States. The officers of FS&L want to analyze the efficiency of the various branch offices using DEA. The following data has been selected to represent appropriate input and output
The Ryder Cup is a three-day golf tournament played every other year with 12 of the best U.S. golfers against 12 of the best European golfers. They play 16 team matches (each match has two U.S. golfers against two European golfers) on Friday and Saturday, and they play 12 singles matches (each
In most of the Walton Bookstore examples in Chapter 10, we assumed that there was a single product. Suppose instead that a company sells two competing products. Sales of either product tend to take away sales from the other product. That is, the demands for the two products are negatively
A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be at least 80% chemical 1, and drug 2 must be at least 50% chemical 2. Up to 70,000 ounces of drug 1 can be sold at $40 per ounce; up to 50,000 ounces of drug 2 can be sold at $25 per ounce. Up to 45,000 ounces of
Many Wall Street firms use LP models to select a desirable bond portfolio. The following is a simplified version of such a model. Solodrex is considering investing in four bonds; $1 million is available for investment. The expected annual return, the worst-case annual return on each bond, and the
A furniture company manufactures tables and chairs. A table requires 45 board-feet of wood, and a chair requires 20 board-feet of wood. Wood can be purchased at a cost of $1.90 per board-foot, and 25,000 board-feet of wood are available for purchase. It takes 2.5 hours of skilled labor to
Capsule Drugs manufactures two drugs. The drugs are produced by blending two chemicals. By weight, drug 1 must contain at least 75% chemical 1, and drug 2 must contain at least 45% chemical 1. Drug 1 sells for $10 per ounce, and drug 2 sells for $7 per ounce. Chemicals 1 and 2 can be produced by
An automobile manufacturing company has a $500,000 advertising budget. To increase its automobile sales, the company is considering advertising in newspapers and on television. The more the company uses a particular medium, the less effective each additional ad is. The file P04_96.xlsx lists the

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Practical Management Science 6th Edition Wayne L. Winston, Christian Albright - Solutions

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