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Questions and Answers of Statistics

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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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 -
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
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
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
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
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
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
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
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,
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.
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
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
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;
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
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
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
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.
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
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
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
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,
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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.
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
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.
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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,
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,
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
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
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

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