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Quantitative Methods For Business 5th Edition Donald Waters - Solutions
Martha Berryman finds that the unit cost of using production equipment is:Cost = 1.5x2 − 120x + 4,000Where x is the number of units produced. Draw a graph to find the lowest unit cost. What production level does this correspond to?
Compare the graphs of y = 2x and y = 3x.
Draw a graph of y = 1/x for values of x between −5 and +5.
If you leave £100 in the bank earning 6% interest, at the end of n years you will have 100 × 1.06n. Draw a graph of this amount over the next 20 years.
Use graphs to solve these simultaneous equations:(a) a + b = 3 and a − b = 5(b) 2x + 3y = 27 and 3x + 2y = 23
Sven Hendriksson finds that one of his productivity measures is related to the number of employees, e, and the production, n, by the equations:10n + 3e = 45 and 2n + 5e = 31What are the current values for e and n? Discuss.
Where does the line y = 20x + 15 cross the line y = 2x2 − 4x + 1?
Where does the line y = e2x cross the line y = x2 + 10?
Find some examples of graphs presented in newspapers and magazines. Describe some that are particularly good, and others that are particularly bad. What can the producers of the bad ones learn from those who presented the good ones?
Spreadsheets are a convenient way of drawing graphs, but there are more specialised graphics packages. What additional features do these specialised packages have? Do a small survey of packages, comparing their graphics features. What other features would you like?
1. How can NWB collect data on potential sales of its Vegan Veggie Bar? What secondary data is available? What primary data do they need, and how should they collect it?2. Design a plan for NWB’s data collection including timing, costs and assumptions.Natural Wholemeal Biscuits (NWB) make a range
How would you describe the following data?(a) Weights of books posted to a bookshop(b) Numbers of pages in books(c) Position of football teams in a league(d) Opinions about a new novel.
What is the appropriate population to give data about the following?(a) Likely sales of a computer game(b) Problems facing small shopkeepers(c) Parking near a new shopping mall(d) Proposals to close a shopping area to all vehicles.
Describe a sampling procedure to find reliable data about house values around the country.
Auditors want to select a sample of 300 invoices from the 9,000 available. How could they do this?
Use a computer to generate a set of random numbers. Use these to design a sampling scheme to find the views of passengers using a low-cost airline.
The readership of a Sunday newspaper has the following characteristics.What are the quotas for a sample of 2,000 readers? Design a spreadsheet to find the quotas in each category for different samplesizes.
Design a survey of the way that companies use the Web in your area. What kind of companies forms your population? How can you select an unbiased sample from these? What data would you want and how would you collect it? What problems might you meet?
Use government statistics to see how the gross national product has changed over the past 30 years. How does this compare with other countries? What other international comparisons can you make?
If you were Hari Chandrasan how would you put the figures into a suitable format for the presentation?High Acclaim Trading is based in Delhi, from where it has rapidly increased its international operations in recent years. A group of influential shareholders recently asked the finance director to
A question in a survey gets the answer ‘Yes’ from 47% of men and 38% of women, ‘No’ from 32% of men and 53% of women, and ‘Do not know’ from the remainder. How could you present this effectively?
The number of students taking a course in the past 10 years is summarised in the following table. Use a selection of graphical methods to summarise this data. Which do you think is thebest?
The following table shows the quarterly profit in millions of dollars reported by the Lebal Corporation, and the corresponding closing share price quoted in cents on the Toronto Stock Exchange. Design suitable formats for presenting thisdata.
The following table shows the number of people employed by Testel Electronics over the past 10 years. How can you present thisdata?
Four regions of Yorkshire classify companies according to primary, manufacturing, transport, retail and service. The number of companies operating in each region in each category is shown in the following table. Show these figures in a number of different barcharts.
Jefferson Chang recorded the average wages of 45 people as follows:Draw a frequency table, histogram, percentage frequency and cumulative frequency table of thisdata.
Draw a histogram of the following data. Class FrequencyLess than 100 ............... 120100 or more, and less than 200 ........ 185200 or more, and less than 300 ........ 285300 or more, and less than 400 ........ 260400 or more, and less than 500 ........ 205500 or more, and less
Draw an ogive of the data in Problem 5.8.
The wealth of a population is described in the following frequency distribution. Draw Lorenz curves and other diagrams to represent thisdata.
The following table shows last year’s total production and profits (in consistent units) from six factories. Use a graphics package to explore the ways that you can present thisdata.
Do a small survey of graphics packages and find one that you prefer. Why do you find this better than the others? Explore the different formats that it can produce for diagrams.Compare this with Excel, which has 30 chart types and many variations.
Mary needs a way of presenting these figures to her employers in a form that they will understand. How do you think she should set about this?When people buy things, they have a number of statutory rights. A basic right is that the product should be of adequate quality and fit for the purpose
When Winnie Mbecu was in hospital for two weeks, the numbers of visitors she received on consecutive days were 4, 2, 1, 5, 1, 3, 3, 5, 2, 1, 6, 4, 1 and 4. How would you describe this data?
Find the mean, median and mode of the following numbers. What other measures can you use?24 26 23 24 23 2427 26 28 25 21 22 25 23 2629 27 24 25 24 24 25
What measures can you use for the following discrete frequencydistribution?
What measures can you use for the following continuous frequencydistribution?
How would you describe the followingdata?
The Langborne Hotel is concerned about the number of people who book rooms by telephone but do not actually turn up. The following table shows the numbers of people who have done this over the past few weeks. How can they summarise thisdata?
In Research project 5.2 we described a set of data that had been collected by Jan Schwartzkopf. What numerical summaries can you use for this data?
Spreadsheets have procedures for automatically describing data, such as the 'Data Analysis' tool in Excel (if this is missing you have to load the Analysis ToolPac as an add-in). An option in this is 'Descriptive Statistics' which automatically finds 13 measures for a set of data (illustrated in
1. If you were Turek Camalli, how would you start thinking about this problem?2. What other data would you like to see and how can this be collected?In 2003 Heinz Muller Engineering had some problems with industrial relations and productivity. By 2010 it tried hard to overcome these and made a
The price of an item in consecutive months has been £106, £108, £111, £112, £118, £125, £130 and £132. Use an index based on the first month to describe these changes. How would this compare with an index based on the final month?
The numbers of fishing boats operating from Porto Novapietro over the past 10 years were: 325 321 316 294 263 241 197 148 102 70Describe these changes by indices based on the first and last year's figures.
The number of people employed by Westbury Cladding over the past 12 months is as follows.Use an index to describe thesefigures.
The annual output of a company is described by the following indices:If the company made 23,850 units in year 2, how many did it make in the other years? What is the percentage increase in output eachyear?
ARP insurance company uses an index to describe the number of agents working for it. This index was revised five years ago, and had the following values over the past 10 years:If the company had 645 agents in year 4, how many did it have in the otheryears?
Employees in a company are put into four wage groups. During a three-year period the numbers employed in each group and the average weekly wage are as follows.Use different indices to describe the changes in wages paid and the numbersemployed.
The following table shows the price of drinks served in The Lion Inn. How would you describe the pricechanges?
A company buys four products with the following characteristics.Calculate a base-weighted index and a current-weighted index for theproducts.
The average prices for four items over four years are as follows.A company annually bought 400, 300, 800 and 200 units of each item respectively. Calculate weighted price indices for years 2 to 4, taking year 1 as the baseyear.
Calculate appropriate indices for the data in the tablebelow.
The following table shows the UK€™s Retail Price Index from 1970 to 2009. As you can see, the index was reset to 100 in January 1974, and again in January 1987.What is the annual rate of inflation for each year? The UK government publishes several values for inflation, each of which is
1. If Janet asks for your advice, how would you summarise her main options? What analyses would help her?2. Based on the information available, what recommendations would you make?3. What other information would you need to make a reasoned decision?Janet Simmons used to work from home and did a lot
A family doctor sees patients for an average of 10 minutes each. There is an additional 5 minutes of paperwork for each visit, so she makes appointments at 15-minute intervals for 5 hours a day. During one surgery the doctor was called away for an emergency that lasted an hour and patients who had
ABC Taxis has an average fixed cost of £9,000 a year for each car. Each kilometre driven has variable costs of 40 pence and collects fares of 60 pence. How many kilometres a year does each car have to travel before making a profit? Last year each car drove 160,000 kilometres.What does this tell
Air Atlantic is considering a new service between Paris and Calgary. It can use existing aeroplanes, each of which has a capacity of 240 passengers, for one flight a week with fixed costs of $90,000 and variable costs amounting to 50% of ticket price. If the airline plans to sell tickets at $600
A company can introduce only one new product from three available. If it estimates the following data, which product would you recommend?
How much will an initial investment of $1,000 earning interest of 8% a year be worth at the end of 20 years? How does this change if the interest is paid more frequently?
Several years ago John McGregor bought an endowment insurance policy that is about to mature. He has the option of receiving £20,000 now or £40,000 in 10 years' time. Because he has retired and pays no income tax, he could invest the money with a real interest rate expected to remain at 10% a
Mitsushama Systems buys new development machines for ¥150,000 each and these are used within the company for 6 years. If they have a resale value of ¥40,000, what is their value at the end of each year with straight-line depreciation? How does this compare with the values from reducing-balance
A company makes fixed annual payments to a sinking fund to replace equipment in 5 years' time. The equipment is valued at £100,000 and interest rates are 12%. How much should each payment be? How would these payments change if the company could put an initial £10,000 into the fund?
How much would the monthly repayments be on a mortgage of €100,000 taken out for 25 years at an interest rate of 12% a year?
Suppose that you are about to buy a new car. You have decided on the model, which costs £12,000. The supplier gives you an option of either a 5-year car loan at a reduced APR of 7%, or £1,250 in cash and a 5-year car loan with an APR of 10%. Which choice is the better? If you depreciate the car
Given the following cash flows for four projects, calculate the net present value using a discount rate of 12% a year. What are the internal rates of return for theprojects?
How does the net present value of the following net cash flows change with discount rate? What is the internal rate ofreturn?
Spreadsheets have a range of standard functions and procedures for financial calculations. We have already mentioned some of these, including Excel’s NPV, IRR, FV, PV, PMT and NPER. Explore the financial functions that are available in a spreadsheet. Check the calculations in this chapter and
Imagine that you want a mortgage to buy a house. Many finance companies can lend you the money, but they quote widely differing terms and conditions. Collect information about offers currently advertised. How can you compare these? Which seems to be the best?
1. Having collected this data, how can the hospital present it in a useful format that is clear and easy to understand?2. Which factors can it use to predict nurses’ grades? What other factors might be relevant?3. What do you think the hospital should do next?Each term, the Western General
The productivity of a factory has been recorded over 10 months, together with forecasts made the previous month by the production manager, the foreman and the Management Services Department. Compare the accuracy of the three sets offorecasts.
Find the line of best fit through the following data. How good is thisfit?
Blaymount Amateur Dramatic Society is staging a play and wants to know how much to spend on advertising. Its objective is to attract as many people as possible, up to the hall capacity. For the past 11 productions their spending on advertising (in hundreds of pounds) and total audience are shown in
Ten experiments were done to find the effects of bonus rates paid to the sales team. What is the line of best fit through the following results? How good is thefit?
Monthly sales for Sengler Marketing for the past year are:6 21 41 75 98 132 153 189 211 243 267 301Use linear regression to forecast sales for the next year. How reliable are these figures?
Jamie O’Connor appraises his employees using the views of two managers. In one department the two managers rank staff as follows. How reliable does this schemeseem?
A food company wanted to know if the amount of taste enhancer added to one of its products has any effect. It ran a test by adding eight different amounts and asking a panel of tasters to rank the results. Does there seem to be a relationship between the amount of enhancer andtaste?
Use multiple regression to find the line of best fit through the following data. What does this tellyou?
What is the best line through the followingdata?
How could you fit a curve through the followingpoints?
A company records sales of four products over a 10-month period. What can you say aboutthese?
The daily number of flights from Skorgaard Airport over a typical summer period are as follows:Analyse these figures and forecast the future numbers of flights. How does this pattern compare with the numbers of flights from otherairports?
1. What information has Piotr collected and how useful is it? What other information does he need?2. How can Piotr forecast future workloads in the purchasing department? How reliable are the results? Do they suggest any patterns of workload?3. What are the implications of Piotr's work, and what
Use linear regression to forecast values for periods 11 to 13 for the following timeseries.
Use simple averages to forecast values for the data in Problem 10.1. Which method gives better results?
Use a 4-period moving average to forecast values for the data in Problem 10.1.
Find the 2-, 3- and 4-period moving averages for the following time series, and use the errors to say which gives the bestresults.
Use exponential smoothing with ( = 0.1 and 0.2 to forecast values for the data in Problem 10.4. Which smoothing constant gives better forecasts? How would you monitor the results with a tracking signal?
Use exponential smoothing with 2 between 0.1 and 0.4 to get forecasts one period ahead for the following time series. Use an initial value of F1 = 208 and say which value of ( isbest.
Balliol.com recorded their opening share price for 12 consecutive weeks. Deseasonalise their results and identify the underlying trend. Forecast values for the next 6weeks.
Use a multiplicative model to forecast values for the next 6 periods of the following timeseries.
Use a multiplicative model to forecast values for the next eight periods of the following timeseries.
Use additive models to forecast values for the time series in Problems 10.8 and 10.9.
In this chapter we have used spreadsheets for doing most of the calculations. Spreadsheets - or specialised add-ins - have standard functions for forecasting, typically including regression, simple averages, moving averages and exponential smoothing. Design a spreadsheet that uses these for a
Governments routinely collect huge amounts of data that they often present in extended time series - giving figures for populations, gross domestic product, employment etc. Collect a reasonably long set of data, and see how well standard forecasting methods work. How can the forecasts be improved?
Energy consumption around the world is rising. Find some figures to describe this growth. Now forecast the future demand for electricity. How accurate are your results? What other factors should be taken into account? What are the implications of your findings?
1. Elemental Electronics works in a very competitive industry. Their operations manager has suggested that they should use linear programming more explicitly in their production planning. With the limited information about their operations, could you build a case to support the operations manager's
Two additives, X1 and X2, can be used to increase the octane number of petrol. 1 kilogram of X1 in 5,000 litres of petrol increases the octane number by 10, while 1 kilogram of X2 in 5,000 litres increases the octane number by 20. The total additives must increase the octane number by at least 5,
North Penberthy Housing Association is planning a number of blocks of flats. Five types of block have been designed, containing flats of four categories (1 - senior citizens, 2 - single person, 3 - small family and 4-large family).The number of flats in each block, and other relevant information,
Jane MacFarlane wants a weekly schedule for two business services, X and Y. Each 'unit' of X delivered to customers needs one service package, while each unit of Y uses two of the packages, and Jane has a maximum of 80 packages available a week. Each unit of X and Y needs 10 hours of subcontracted
Novacook Ltd makes two types of cooker, one electric and one gas. There are four stages in the production of each of these, with the following features:Each electric cooker has a variable cost of £200 and a selling price of £300, and each gas cooker has a variable cost of £160 and a
Tarsands Oil make two blends of fuel by mixing three crude oils. The costs and daily availability of the oils are:Tarsands sell each litre of Blend 1 for $1.00 and each litre of Blend 2 for $1.20. Long-term contracts require at least 10,000 litres of each blend to be produced. What should
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