# Round all probability calculations to 2 decimal places

January 30, 2017

Question
QUESTION 2 Decision Analysis

Show all calculations to support your answers. Round all probability calculations to 2 decimal places.

John Carpenter runs a timber company. John is considering an expansion to his product line by manufacturing a new product, garden sheds. He would need to construct either a large new plant to manufacture the sheds, or a small plant. He decides that it is equally likely that the market for this product would be favourable or unfavourable. Given a favourable market he expects a profit of \$200,000 if he builds a large plant, or \$100,000 from a small plant. An unfavourable market would lead to losses of \$180,000 or \$20,000 from a large or small plant respectively.

(a) 2 marks
Construct a payoff matrix for John’s problem. If John were to follow the EMV criterion, show calculations to indicate what should he do, and why?

(b) 2 marks
What is the expected value of perfect information and explain the reason for such a calculation?

John has the option of conducting a market research survey for a cost of \$10,000. He has learned that of all new favourably marketed products, market surveys were positive 70% of the time but falsely predicted negative results 30% of the time. When there was actually an unfavourable market, however, 80% of surveys correctly predicted negative results while 20% of surveys incorrectly predicted positive results.

(c) 4 marks
Using the market research experience, calculate the revised probabilities of a favourable and an unfavourable market for John’s product given positive and negative survey predictions.

(d) 4 marks
Based on these revised probabilities what should John do? Support your answer with EVSI and ENGSI calculations.

(e) 8 marks
The decision making literature mostly adopts a rational approach. However, Tversky and Kahneman (T&K) (Reading 3.1) adopt a different approach, arguing that often people use other methods to make decisions, relying on heuristics.

What do they mean by the term heuristics? (2 marks)

Describe three types of heuristicsthat T&K suggest people use in judgments under uncertainty. (3 marks)

Give one example from your own experience of a biasthat might result from eachof these heuristics. (3 marks)

QUESTION 3

Dr Catscan is an ophthalmologist who, in addition to prescribing glasses and contact lenses, performs laser surgery to correct myopia. This laser surgery is fairly easy and inexpensive to perform.

To inform the public about this procedure Dr Catscan advertises in the local paper and holds information sessions in her office one night a week at which she shows a videotape about the procedure and answers any questions potential patients might have.

The room where these meetings are held can seat 10 people, and reservations are required. The number of people attending each session varies from week to week. Dr Catscan cancels the meeting if 2 or fewer people have made reservations.

Using data from the previous year Dr Catscan determined that reservations follow this pattern:

Number of reservations

0

1

2

3

4

5

6

7

8

9

10

Probability

0.02

0.05

0.08

0.16

0.26

0.18

0.11

0.07

0.05

0.01

0.01

Using the data from last year Dr Catscan determined that 25% of the people who attended information sessions elected to have the surgery performed. Of those who do not, most cite the cost of the procedure (\$2,000 per eye, \$4,000 in total as almost everyone has both eyes done) as their major concern. The surgery is regarded as cosmetic so that the cost is not covered by Medicare or private hospital insurance funds.

Dr Catscan has now hired you as a consultant to analyse her financial returns from this surgery. In particular, she would like answers to the following questions, which you are going to answer by building an Excel model to simulate 20 weeks of the practice. Random numbers must be generated in Excel and used with the VLOOKUP command to determine the number of reservations,0 and there must be no data in the model itself. The same set of random numbers should be used for all three parts. An IF statement is required for part (a) to determine attendance each week, given cancellation of meetings.

(a) 10 marks
On average, how much revenue does Dr Catscan’s practice in laser surgery earn each week? If your simulation shows a fractional number of people electing surgery use such fractional values in determining revenue. Paste your model results into Word including a copy of formulas with row and column headings.

(b) 3 marks
Adjust your model to determine on average, how much revenue would be generated each week if Dr Catscan did not cancel sessions with 2 or fewer reservations? Paste results into Word.

(c) 3 marks
Dr Catscan believes that 35% of people attending the information sessions would have the surgery if she reduced the price to \$1,500 per eye or \$3,000 in total. Under this scenario how much revenue per week could Dr Catscan expect from laser surgery? Modify your Excel model to answer this and paste results into Word.

(d) 4 marks
Write a brief report with your recommendations to Dr Catscan on the most appropriate strategy.

QUESTION 4 Regression Analysis and Cost Estimation 20 marks

The CEO of Carson Company has asked you to develop a cost equation to predict monthly overhead costs in the production department. You have collected actual overhead costs for the last 12 months, together with data for three possible cost drivers, number of Indirect Workers, number of Machine Hours worked in the department and the Number of Jobs worked on in each of the last 12 months:

Indirect Workers

Machine Hours

Number of Jobs

\$2,200

30

350

1,000

4,000

35

500

1,200

3,300

50

250

900

4,400

52

450

1,000

4,200

55

380

1,500

5,400

58

490

1,100

5,600

90

510

1,900

4,300

70

380

1,400

5,300

83

350

1,600

7,500

74

490

1,650

8,000

100

560

1,850

10,000

105

770

1,250

(a) 5 marks
The CEO suggests that he has heard that the high-low method of estimating costs works fairly well and should be inexpensive to use. Write a response to this suggestion for the CEO indicating the advantages and disadvantages of this method. Include the calculation of a cost equation for this data using Machine Hours as the cost driver.
(b) 5 marks
Using Excel develop three scatter diagrams showing overhead costs against each of the three proposed independent variables. Comment on whether these scatter diagrams appear to indicate that linearity is a reasonable assumption for each.

(c) 5 marks
Using the regression module of Excel’s Add-in Data Analysis, perform 3 simple regressions by regressing overhead costs against each of the proposed independent variables. Show the output for each regression and evaluate each of the regression results, indicating which of the three is best and why.

Provide the cost equations for those regression results which are satisfactory and from them calculate the predicted overhead in a month where there were 100 Indirect Workers and 500 Machine Hours and 1,000 Jobs worked.

(d) 5 marks
Selecting the two best regressions from part (c) conduct a multiple regression of overhead against these two independent variables. Evaluate the regression results.

Draw conclusions about the best of the four regression results to use.

QUESTION 5

(a) 5 marks

All forecasts are never 100% accurate but subject to error.

How is forecast error calculated? (1 mark)
Identify and describe three common measures of forecast error. Then illustrate how each is calculated by constructing a 4-period example. (4 marks)

(b) 10 marks as indicated below

Consider the following table of monthly sales of car tyres by a local company:

Month

Unit Sales

January

400

February

500

March

540

April

560

May

600

June

?

(i) 3 marks

Using a 2-month moving averagedevelop forecasts sales for March to June inclusive.

(ii) 3 marks

Using a 2-month weighted moving average, with weights of 2 for the most recent month and 1 for the previous month develop forecasts sales for March to June inclusive.

(iii) 3 marks

The sales manager had predicted sales for January of 400 units. Using exponential smoothingwith a weight of 0.3 develop forecasts sales for March to June inclusive.

(iv) 1 mark

Which of the three techniques gives the most accurate forecasts? How do you know?

(c) 5 marks

Describe the four patterns typically found in time series data. What is meant by the expression “decomposition” with regard to forecasting? Briefly describe the process.

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