DECISION SUPPORT TOOLS
QUESTION 1 Probability
Show all calculations/reasoning
(a) What are the two basic laws of probability?
(b) What is a random variable? What are the various types of random variables?
(c) Consider the following record of sales for a product for the last 100 days.
SALES UNITS NUMBER OF DAYS
0 10
1 25
2 30
3 25
4 10
100
1. What was the probability of selling 2 or 3 units on any one day?
2. What were the average daily sales units?
3. What was the probability of selling 3 units or more?
4. What was the probability of selling 2 units or less?
(d) An urn contains 20 marbles. 6 are red, 10 are green and 4 are blue. Marbles are drawn and then replaced after each draw.
Calculate the probability of drawing:
(i) a blue marble on the first draw
(ii) a blue marble on the first draw and a red on the second draw
(iii) two green marbles in two draws
(iv) red marble on the second draw given a blue on the first draw
(e) The time to complete a construction project is normally distributed with a mean of 80 weeks and a standard deviation 8 weeks.
(i) What is the probability that the project will be completed in 84 weeks or less?
(ii) What is the probability that the project will be completed in 92 weeks or less?
(iii) What is the probability that the project will take longer than 90 weeks?
(f) 1. Search the Internet for the latest figures you can find on the age and sex of the Australian population.
2. Then using Excel, prepare a table of population numbers (not percentages) by sex (in the columns) and age (in the rows). Break age into about 5 groups, e.g. 0-14, 15-24, 15-54, 55-64, 65 and over. Insert total of each row and each column. Past the table into Word as a picture.
Give the table a title, and below the table quote the source of the figures.
3. Calculate from the table, showing your calculation methods:
• The marginal probability that any person selected at random from the population is a male.
• The marginal probability that any person selected at random from the population is aged between 25 and 54.
• The joint probability that any person selected at random from the population is a female and aged between 55 and 64.
• The conditional probability that any person selected at random from the population is 25 or over given that the person is a male.
QUESTION 2 Statistical Decision Making and Quality Control
Show all calculations/reason
(a) A company wishes to set control limits for monitoring the direct labour time to produce an important product. Over the past, the mean time has been 45 minutes with a standard deviation of 15 minutes and is believed to be normally distributed. The company proposes to collect random samples of 36 observations to monitor labour time.
1. If management wishes to establish x ¯ control limits covering the 95% confidence interval, calculate the appropriate UCL and LCL.
2. If management wishes to use smaller samples of 16 observations calculate the control limits covering the 95% confidence interval. (Round calculations to 2 decimal places)
(b) Quality control chart
Using the Excel Chart function prepare a quality control chart from the following sequential monthly cycle time data. The desired level of performance is 140, with an upper control limit of 160 and a lower control limit of 120.
Month Average Cycle Time
(Hours)
January 124
February 175
March 147
April 97
May 153
June 132
July 228
August 152
September 172
October 112
November 138
December 141
Explain whether the process is in control or whether corrective action is required.
Justify your conclusion.
QUESTION 3 Decision Analysis
Show all calculations to support your answers. You may follow the methods shown in the mp4 on Decision Analysis for a way to do part (b) of this question if you wish.
(a) Distinguish between decision making under certainty and decision making under uncertainty. To what aspects of the decision does the uncertainty refer? What other possible sources of uncertainty are there in decision making?
(b) Joe Black runs a manufacturing business. Because of competition in his market Joe is considering purchasing one of three new types of equipment, A, B or C. The conditional profits from each given favourable or unfavourable markets are as follows:
Favourable Unfavourable
Market Market
Equipment $ $
A 300,000 -200,000
B 250,000 -100,000
C 75,000 -18,000
(i) If Joe is an optimist which type of equipment should he buy?
(ii) If Joe is a pessimist which type of equipment should he buy?
(iii) Following the criterion of regret which type of equipment should he buy?
(iv) If Joe believes that there is a 70% chance of the market being favourable which type of equipment should he buy?
(c) The management of Wildcat Drilling N.L. is considering the purchase of an oil exploration lease over a parcel of land, for $200,000. If the lease is purchased a test well could be drilled at a cost of $1,500,000. If the test well proved dry the lease would be abandoned. If the well brought in oil the lease could be sold immediately for $18,000,000. On known information the probability that the well would prove dry is assessed at 0.95.
The manager has absolute faith in the ability of a mystic, Bill Diviner, who for a fee of $500,000 can give a perfect prediction as to whether the well would be a success or dry.
Required:
Draw a decision tree showing the choices available to the manager of Wildcat and the merits of each. What should the management do?
QUESTION 4 Value of information
Show all calculations to support your answers. You may follow the methods shown in the mp4 on Value of info for a way to answer this question if you wish.
(a)
A firm is considering the marketing of a new product which will either be a success or a failure. The prior probability of success is judged to be 0.3. If the product is marketed and is a success the firm expects to earn $500,000, while a failure is expected to lead to a loss of $300,000.
(i) Should the product be marketed? Why?
(ii) What is the expected value of perfect information about the success or failure of the product?
The firm is considering a market survey whose results can be classified as favourable, neutral or unfavourable (meaning that you will have to prepare 3 lots of revisions of probability, one for each signal). Some of the conditional probabilities are:
p(favourable|success) = 0.6
p(neutral|success) = 0.3
p(neutral|failure) = 0.2,
p(unfavourable|failure) = 0.7.
(iii) What is the posterior probability of success given a favourable survey result?
(iv) What is the maximum the firm should be willing to pay for the market survey?
QUESTION 5 Simulation
This is a work integrated assessment item. The tasks are similar to what would be carried out in the workplace.
The Bandicoots Football Club gains significant revenue from ticket sales at each game played at home during the season. The sale of programs for these games also adds to profitability. Each program costs $2.00 to produce and sells for $5.00. Any programs unsold at the end of any game are sent to a recycling centre and do not produce any revenue.
Records of the programs sold for each game show the following:
Number of Programs Sold Probability
2300 0.10
2400 0.20
2500 0.30
2600 0.25
2700 0.15
(a) Your manager has asked you as the management accountant for the club to determine the profitability of program production. In particular you have been asked to investigate two strategies where the number of programs to be printed are either 2500 or 2600. You decide to use Excel to simulate the sale of programs at 10 games in a season together with the profit or loss on programs for each game when (1) 2500 and (2) 2600 programs are printed. Include a calculation of the total profit/loss for the season and the average profit/loss per game.
Hints: Your model should have 8 columns: Game #, RN Sales, Demand, Production #, Sales Units, Sales Revenue, Production Costs, Profit/Loss. The model must be completely formula driven - there must be no data in the model or the model formulas – all data should be in a data input section above the model. An IF or MIN function is required in the formulas in the Sales Units column. After completing the model you can vary the results by pressing F9 (recalculate) a number of times to view such variations resulting from changes in the random numbers generated.
Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show row and column numbers and be copied from Excel into Word. See Spreadsheet Advice in Interact Resources for guidance.
(b) To check on hour simulation conclusions use marginal analysis to determine the optimum number of programs to print.
(c) Write a report to your manager explaining which of the two production strategies you would recommend and why. You may support your report by including reference to the profits under each strategy, noting any limitations to the methods you have adopted to analyse the situations.
The report must be dated, addressed to the Manager and signed off by you.
(Word limit: No more than 150 words)
QUESTION 6 Regression Analysis and Cost Estimation
Acme Company is trying to estimate the behaviour of overhead costs. Data for the last 10 months has been collected, together with possible cost drivers, as follows (DLH = direct labour hours, MH = machine hours):
Month Overhead DLH MH
1 $ 7,200 201 220
2 $ 7,400 250 240
3 $ 8,300 300 340
4 $ 8,500 350 350
5 $ 7,000 200 180
6 $ 8,800 400 440
7 $ 9,600 450 470
8 $ 8,600 350 340
9 $ 10,000 500 510
10 $ 7,900 300 330
(a) Using the High-Low method of cost estimation and DLH as the cost driver, what would be the overhead cost equation?
(b) Using Excel, perform three regression analyses to regress overhead cost against DLH, then MH, then against both of them simultaneously. State the cost equation from each. Analyse and comment on the results of each regression as you perform it and determine the best one to use as a basis for future use.
(c) If the simple regression using DLH were adopted, what would be the predicted overhead in a month when there were 400 DLH and 500 MH used?
QUESTION 7 CVP Analysis
(a) CVP Ltd has a monthly sales volume of $75,000 for its only product. Variable costs are $45,000 and monthly fixed costs are $7,500.
Required:
i. Monthly breakeven point in sales dollars.
ii. The required level of sales to yield a monthly profit of $25,000 before tax.
iii. The profit before tax expected in a month in which sales of $80,000 are realised.
iv. The unit sales volume required to earn an after-tax monthly profit of $42,000 given a sales price of $20 per unit and a company tax rate of 30c in the dollar.
(b) A company makes two products, X and Y. At present the sales mix is 1 unit of X to 3 units of Y. Fixed costs per period are $20,000. Selling prices and variable costs per unit for each product are:
X Y
Unit selling price $18 $15
Unit variable cost $10 $11
Required:
i. Given this sales mix, how many units of each product must be sold in a period to make a profit of $15,000 before tax?
ii. If in a period the sales mix changed to 2 units of X to 2 units of Y, and the total number of units sold in the period were 8,000, how much profit would be earned in the period?
(c) Alpha Company produces a single product, Beta, which has the following unit selling price and costs:
Selling price per unit $2000
Variable costs per unit $1500
Fixed costs per annum $2 000 000
Prices and costs are certain, but annual demand is uncertain. It is thought that annual demand is normally distributed with expected sales of 6000 units and a standard deviation of 1000 units.
Required:
i. Calculate expected annual profit.
ii. What is the standard deviation of expected profit?
iii. Calculate the probability of at least breaking even using the probability distribution of profits.
POINTS TO BE NOTICED WHILE ASSIGNMENT :
Dear Students,
Feel free to use the ABS / similar site to get the data for Q 1 f, as listed in the Assignment .
Here is a sample, from ABS site, for reference
Age Group Male Female
0-4 years 729,971 691,080
5-9 years 694,560 657,362
10-14 years 703,307 667,750
15-19 years 722,378 683,416
20-24 years 741,120 719,554
25-29 years 754,467 758,770
30-34 years 719,655 734,121
35-39 years 747,117 773,020
40-44 years 754,568 788,310
45-49 years 740,961 763,179
50-54 years 711,742 735,662
55-59 years 637,839 659,405
60-64 years 597,884 608,232
65-69 years 455,419 463,899
70-74 years 342,691 365,397
75-79 years 252,929 292,333
80-84 years 188,242 248,695
85-89 years 100,804 169,995
90-94 years 31,793 71,981
95-99 years 5,909 18,925
100 years and over 657 2,620
Total 10,634,013 10,873,706
Data Source: 2011
• The question should add that -Bill Diviner would not be allowed on the land unless the lease is purchased first-. Can you please amend the data acordingly?
GET ANSWERS / LIVE CHAT