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Data Analysis And Decision Making 4th Edition Christian Albright, Wayne Winston, Christopher Zappe - Solutions

A shipping company is attempting to determine how its shipping costs for a month depend on the number of units shipped during a month. The number of units shipped and total shipping cost for the last 15 months are given in the file S12_63.xlsx.a. Determine a relationship between units shipped and
Consider a monthly series of air conditioner (AC) sales. In the discussion of Winters’ method, a monthly seasonality of 0.80 for January, for example, means that during January, AC sales are expected to be 80% of the sales during an average month. An alternative approach to modeling seasonality,
Winters’ method assumes a multiplicative seasonality but an additive trend. For example, a trend of 5 means that the level will increase by five units per period. Suppose that there is actually a multiplicative trend. Then (ignoring seasonality) if the current estimate of the level is 50 and the
Consider the file S12_59.xlsx, which contains total monthly U.S. retail sales data. Does a regression approach for estimating seasonality provide forecasts that are as accurate as those provided by (a)Winters’ method and (b) the ratio-to-moving-average method? Compare the summary measures of
The file S12_56.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). Does a regression approach for estimating seasonality provide forecasts that are
The file S12_68.xlsx contains monthly data on consumer revolving credit (in millions of dollars) through credit unions.a. Use these data to forecast consumer revolving credit through credit unions for the next 12 months. Do it in two ways. First, fit an exponential trend to the series. Second, use
The file S12_69.xlsx contains net sales (in millions of dollars) for Procter & Gamble.a. Use these data to predict Procter & Gamble net sales for each of the next two years. You need consider only a linear and exponential trend, but you should justify the equation you choose.b. Use your
The file S12_70.xlsx lists annual revenues (in millions of dollars) for Nike. Forecast the company’s revenue in each of the next two years with a linear or exponential trend. Are there any outliers in your predictions for the observed period?
The file S11_44.xlsx contains data on pork sales. Price is in dollars per hundred pounds sold, quantity sold is in billions of pounds, per capita income is in dollars, U.S. population is in millions, and GDP is in billions of dollars. a. Use these data to develop a regression equation that can be
The file S12_72.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.b. Use simple
The file S12_73.xlsx contains data on monthly U.S. permits for new housing units (in thousands of houses).a. Using Winters’ method, find values of α, β, and γ that yield an RMSE as small as possible. Does this method track the housing crash in recent years?b. Although we have not discussed
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 S11_45.xlsx. Use regression to fit the following model to these data:Yt = a + b1Yt - 1 + b2Pt + etThis equation indicates
The file S12_75.xlsx contains five years of monthly data for a particular company. The first variable is Time (1 to 60). The second variable, Sales1, contains data on sales of a product. Note that Sales1 increases linearly throughout the period, with only a minor amount of noise. (The third
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 S12_77.xlsx contains monthly time series data on corporate bond yields. These are averages of daily figures, and each is expressed as an annual rate.The variables are:• Yield AAA: average yield on AAA bonds• Yield BAA: average yield on BAA bondsIf you examine either Yield variable, you
The file S12_79.xlsx contains data on mass layoff events in all industries in the U.S. There are two versions of the data: non-seasonally adjusted and seasonally adjusted. Presumably, seasonal factors can be found by dividing the non-seasonally adjusted values by the seasonally adjusted values. For
The Eastland Plaza Branch of the Indiana University Credit Union was having trouble getting the correct staffing levels to match customer arrival patterns. On some days, the number of tellers was too high relative to the customer traffic, so that tellers were often idle. On other days, the opposite
Amanta Appliances sells two styles of refrigerators at more than 50 locations in the Midwest. The first style is a relatively expensive model, whereas the second is a standard, less expensive model. Although weekly demand for these two products is fairly stable from week to week, there is enough
Other sensitivity analyses besides those discussed could be performed on the product mix model. Use Solver Table to perform each of the following. In each case keep track of the values in the changing cells and the objective cell, and discuss your findings. a. Let the selling price for Basics vary
In PC Tech’s product mix problem, assume there is another PC model, the VXP that the company can produce in addition to Basics and XPs. Each VXP requires eight hours for assembling, three hours for testing, $275 for component parts, and sells for $560. At most 50 VXPs can be sold.a. Modify the
Continuing the previous problem, perform a sensitivity analysis on the selling price of VXPs. Let this price vary from $500 to $650 in increments of $10, and keep track of the values in the changing cells and the objective cell. Discuss your findings.
Again continuing problem 2, suppose that you want to force the optimal solution to be integers. Do this in Solver by adding a new constraint. Select the changing cells for the left side of the constraint, and in the middle dropdown list, select the “int” option. How does the optimal integer
If all of the inputs in PC Tech’s product mix problem are nonnegative, are there any input values such that the resulting model has no feasible solutions?
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
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?
Again continuing problem 2, perform a sensitivity analysis where the selling prices of Basics and XPs simultaneously change by the same percentage, but the selling price of VXPs remains at its original value. Let the percentage change vary from -25% to 50% in increments of 5%, and keep track of the
Consider the graphical solution to the product mix problem. Now imagine that another constraint—any constraint—is added. Which of the following three things are possible: (1) The feasible region shrinks; (2) The feasible region stays the same; (3) The feasible region expands? Which of the
Modify PC Tech’s product mix model so that there is no maximum sales constraint. Does this make the problem unbounded? Does it change the optimal solution at all? Explain its effect.
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 23 can be considered customer demands that must be met. Make this change and rerun Solver. What do you
Use Solver Table to run a sensitivity analysis on the cost per assembling labor hour, letting it vary from $5 to $20 in increments of $1. Keep track of the computers produced in row 21, the hours used in the range B26:B28, and the total profit. Discuss your findings. Are they intuitively what you
Create a two-way Solver Table for the product mix model, where total profit is the only output and the two inputs are the testing line 1 hours and testing line 2 hours available. Let the former vary from 4000 to 6000 in increments of 500, and let the latter vary from 3000 to 5000 in increments of
Model 8 has fairly high profit margins, but it isn’t included at all in the optimal mix. Use Solver Table, 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.
Suppose that you want to increase all three of the resource availabilities in the product mix model simultaneously by the same percentage. You want this percentage to vary from -25% to 50% in increments of 5%. Modify the spreadsheet model slightly so that this sensitivity analysis can be performed
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
In Solver’s sensitivity report for the product mix model, the allowable decrease for available assembling hours is 2375. This means that something happens when assembling hours fall to 20,000 - 2375 =17,625. See what this means by first running Solver with 17,626 available hours and then again
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 Solver Table and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the changing cells and the objective
Modify the Pigskin model so that there are eight 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 four months in the planning horizon. Do either of these
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
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
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 6. 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 five 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 4. How does this change the optimal
Modify the Pigskin spreadsheet model in the following way. Assume that the timing of demand and production are such that only 70% of the production in a given month can be used to satisfy the demand in that month. The other 30% occurs too late in that month and must be carried as inventory to help
A chemical company manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an hour costs $400 and yields 300 units of A, 100 units of B, and 100 units of C. Running process 2 for an hour costs $100 and yields 100 units of
A furniture company manufactures desks and chairs. Each desk uses four units of wood, and each chair uses three units of wood. A desk contributes $400 to profit, and a chair contributes $250. Marketing restrictions require that the number of chairs produced be at least twice the number of desks
A farmer in Iowa owns 450 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields $2000 profit, requires three workers, and requires two tons of fertilizer. Each acre planted with corn yields $3000 profit, requires two workers, and requires four tons of
During the next four months, a customer requires, respectively, 500, 650, 1000, and 700 units of a commodity, and no backlogging is allowed (that is, the customer’s requirements must be met on time). Production costs are $50, $80, $40, and $70 per unit during these months. The storage cost from
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
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
For a telephone survey, a marketing research group needs to contact at least 600 wives, 480 husbands, 400 single adult males, and 440 single adult females. It costs $3 to make a daytime call and (because of higher labor costs) $5 to make an evening call. The file S13_31.xlsx lists the results that
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 are available. A table requires either 17 board feet of oak or 30 board feet of pine, and a chair
A manufacturing company makes two products. Each product can be made on either of two machines. The time (in hours) required to make each product on each machine is listed in the file S13_33.xlsx. Each month, 500 hours of time are available on each machine. Each month, customers are willing to buy
There are three factories on the Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1500 to process a ton of factory 1 waste, and each ton processed reduces the amount
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
A company manufactures mechanical heart valves from the heart valves of pigs. Different heart operations require valves of different sizes. The company purchases pig valves from three different suppliers. The cost and size mix of the valves purchased from each supplier are given in the file
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
During the next two months an automobile manufacturer must meet (on time) the following demands for trucks and cars: month 1, 400 trucks and 800 cars; month 2, 300 trucks and 300 cars. During each month at most 1000 vehicles can be produced. Each truck uses two tons of steel, and each car uses one
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 demands for shirts and pants must be met (on time): month 1, 1000 shirts and 1500 pairs of pants; month
Each year, a shoe manufacturing company faces demands (which must be met on time) for pairs of shoes as shown in the file S13_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 small appliance manufacturer must meet (on time) the following demands: quarter 1, 3000 units; quarter 2, 2000 units; quarter 3, 4000 units. Each quarter, up to 2700 units can be produced with regular-time labor, at a cost of $40 per unit. During each quarter, an unlimited number of units can be
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 S13_42.xlsx. The machine time (in hours) required to produce a pound of each drug at each city is also shown in this
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 S13_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.
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 steps: stamping, forming, and assembly. In the stamping stage, a large machine is used to stamp
After graduating from business school, George Clark went to work for a Big Six accounting firm in San Francisco. Because his hobby has always been wine making, when he had the opportunity a few years later he purchased five acres plus an option to buy 35 additional acres of land in Sonoma Valley in
In the original Red Brand problem, suppose the plants cannot ship to each other and the customers cannot ship to each other. Modify the model appropriately, and rerun Solver. How much does the total cost increase because of these disallowed routes?
Modify the original Red Brand problem so that all flows must be from plants to warehouses and from warehouses to customers. Disallow all other arcs. How much does this restriction cost Red Brand, relative to the original optimal shipping cost?
In the original Red Brand problem, the costs for shipping from plants or warehouses to customer 2 were purposely made high so that it would be optimal to ship to customer 1 and then let customer 1 ship to customer 2. Use SolverTable appropriately to do the following. Decrease the unit shipping
In the original Red Brand problem the arc capacity is the same for all allowable arcs. Modify the model so that each arc has its own arc capacity. You can make up the arc capacities.
Continuing the previous problem, make the problem even more general by allowing upper bounds (arc capacities) and lower bounds for the flows on the allowable arcs. Some of the upper bounds can be very large numbers, effectively indicating that there is no arc capacity for these arcs, and the lower
Suppose in the original Grand Prix example that the routes from plant 2 to region 1 and from plant 3 to region 3 are not allowed. How would you modify the original model (Figure 14.12) to rule out these routes? How would you modify the alternative model (Figure 14.17) to do so? Discuss the pros and
In the Red Brand two-product problem, we assumed that the unit shipping costs are the same for both products. Modify the spreadsheet model so that each product has its own unit shipping costs. You can assume that the original unit shipping costs apply to product 1, and you can make up new unit
Here is a problem to challenge your intuition. In the original Grand Prix example, reduce the capacity of plant 2 to 300. Then the total capacity is equal to the total demand. Rerun Solver on the modified model. You should find that the optimal solution uses all capacity and exactly meets all
Continuing the previous problem (with capacity 300 at plant 2), suppose you want to see how much extra capacity and extra demand you can add to plant 1 and region 2 (the same amount to each) before the total shipping cost stops decreasing and starts increasing. Use SolverTable appropriately to find
Modify the original Grand Prix example by increasing the demand at each regions by 200, so that total demand is well above total plant capacity. However, now interpret these “demands” as “maximum sales,” the most each region can accommodate, and change the “demand” constraints to become
Modify the original Grand Prix example by increasing the demand at each region by 200, so that total demand is well above total plant capacity. This means that some demands cannot be supplied. Suppose there is a unit “penalty” cost at each region for not supplying an automobile. Let these unit
How difficult is it to expand the original Red Brand model? Answer this by adding a new plant, two new warehouses, and three new customers, and modify the spreadsheet model appropriately. You can make up the required input data. Would you conclude that these types of spreadsheet models scale easily?
In the Red Brand problem with shrinkage, change the assumptions. Now instead of assuming that there is some shrinkage at the warehouses, assume that there is shrinkage in delivery along each route. Specifically, assume that a certain percentage of the units sent along each arc perish in
Consider a modification of the original Red Brand problem where there are N plants, M warehouses, and L customers. Assume that the only allowable arcs are from plants to warehouses and from warehouses to customers. If all such arcs are allowable—all plants can ship to all warehouses and all
Continuing the previous problem, develop a sample model with your own choices of N, M, and L that barely stay within Solver’s limit. You can make up any input data. The important point here is the layout and formulas of the spreadsheet model.
Extend SureStep’s original (no backlogging) aggregate planning model from four to six months. Try several different values for demands in months 5 and 6, and run Solver for each. Is your optimal solution for the first four months the same as the one in the example?
The current solution to Sure Step’s no-backlogging aggregate planning model does quite 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
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 (=1500/160). Suppose workers can change their contract so that they have to work only 7.5 hours per day
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
In the current no-backlogging problem, SureStep doesn’t hire any workers, and it uses almost no overtime. This is evidently because of low demand. Change the demands to 6000, 8000, 5000, and 3000, and rerun Solver. Is there now any hiring and/or overtime? With this new demand pattern, explore the
In the SureStep no-backlogging problem, change the demands so that they become 6000, 8000, 5000, and 3000. Also, change the problem slightly so that newly hired workers take six hours to produce a pair of shoes during their first month of employment. After that, they take only four hours per pair
You saw that the “natural” way to model SureStep’s backlogging problem, with IF functions, leads to a non-smooth model that Solver has difficulty handling. There is another version of the problem that is also difficult for Solver. Suppose SureStep wants to meet all demands on time (no
Modify the Barney-Jones investment problem so that there is a minimum amount that 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
In the Barney-Jones investment problem, 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 account. You can choose any
We claimed that our model for Barney-Jones is generalizable. Try generalizing it to the case where there are two more potential investments, F and G. Investment F requires a cash outlay in year 2 and returns $0.50 in each of the next four years. Investment G requires a cash outlay in year 3 and
In our Barney-Jones spreadsheet model, we ran investments across columns and years down rows. Many financial analysts 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.
In the pension fund problem, suppose there is a fourth bond, bond 4. Its unit cost in 2010 is $1020; it returns coupons of $70 in years 2011 through 2016 and a payment of $1070 in 2017. Modify the model to incorporate this extra bond, and re-optimize. Does the solution change—that is, should
In the pension fund problem, 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 optimize. How much more money does James need to allocate initially?
In the pension fund problem, suppose James has been asked to see how the optimal solution will change if the required payments in years 2017 through 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
Our pension fund model is streamlined, perhaps too much. It does all of the calculations concerning cash flows in row 20. James decides he would like to break these out into several rows of calculations: Beginning cash Amount spent on bonds (positive in 2010 only), Amount received from bonds
Suppose the investments in the Barney-Jones problem 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 2. Does the current model easily accommodate such investments? Try it with
In the pension fund problem, you know that if the amount of money allocated initially is less than the amount found by Solver, 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
Continuing the previous problem in a slightly different direction, continue to use the Money_allocated cell as a changing cell, but add a constraint that it must be less than or equal to any value, such as $195,000, that is less than its current optimal value. With this constraint, James will again
Solve the following modifications of the capital budgeting model in Figure 14.40. a. Suppose that at most two of projects 1 through 5 can be selected.b. Suppose that if investment 1 is selected, then investment 3 must also be selected.c. Suppose that at least one of investments 6 and 7 must be
In the capital budgeting model in Figure 14.40, we supplied the NPV for each investment. Suppose instead that you are given only the streams of cash inflows from each investment shown in the file S14_49.xlsx. This file also shows the cash requirements and the budget. You can assume that (1) All
Solve the previous problem using the input data in the file P14_50.xlsx.In the capital budgeting model in Figure 14.40, we supplied the NPV for each investment. Suppose instead that you are given only the streams of cash inflows from each investment shown in the file S14_49.xlsx. This file also
Solve Problem 49 with the extra assumption that the investments can be grouped naturally as follows: 1–4, 5–8, 9–12, 13–16, and 17–20.a. Find the optimal investments when at most one investment from each group can be selected.b. Find the optimal investments when at least one investment

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