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(a) Explain the process of using marginal analysis to solve decision problems with a square matrix (ie actions = states) involving discrete probability distributions describing the states of nature. What steps are taken in the process, providing your own simple example.
What are the advantages and disadvantages of using marginal analysis to solve decision problems?
(b) James Patterson is considering investing money in three alternative investments over a one-year period. Below are the expected profits from each investment given assumptions about the state of the economy:
Decision Alternative Good Economy Poor Economy
Stock market $160,000 -$40,000
Bonds $60,000 $40,000
Term deposit $46,000 $46,000
(i) If James is an optimist which investment should he choose?
(ii) If James is a pessimist which investment should he choose?
(iii) Following the criterion of regret which investment should he choose?
(iv) If James believes that there is a 70% chance of a good economy which investment should he choose?
(v) What is the expected value of perfect information about the state of the economy?
QUESTION 2 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.
20 marks - 4 for (a), 8 for (b), 2 for (c), 6 for (d)
A manufacturer is trying to choose between two production methods (a1 and a2) for a new product. He considers that the probability of demand for the new product being good (s1) is 0.4 and the probability that demand will be poor (s2) is 0.6.
In evaluating the two production methods the manufacturer has calculated the following table of conditional profits:
a1 $24,000 $15,000
a2 -$4,000 $40,000
(a) Which production method should be used? Show calculations.
The manufacturer asks a marketing consult for an opinion as to whether demand will be good or poor. From previous experience when the consultant has indicated that demand will be good she has been right 80% of the time, and when she has indicated that demand will be poor she has been right 70% of the time.
(b) Revise the prior probabilities in light of the consultant’s track record.
(c) What is the posterior probability of good demand given that the consultant has indicated demand will be good?
(d) What is the expected net gain or loss from engaging the consultant? Should the consultant be engaged? Why?
Show all calculations/reasoning
QUESTION 3 Simulation
This is a work integrated assessment item. The tasks are similar to what would be carried out in the workplace.
20 marks - 10 for (a), 3 for (b), 7 for (c)
A factory has a toolshop in which one person serves toolmakers and is paid $75 per hour. Toolmakers employed by the factory must go to the toolshop for new tools, and are paid $100 per hour. Over a period of time it has been noted that the time between arrivals of toolmakers at the toolshop and the time to serve a toolmaker are as follow:
Time between Arrivals (minutes) Relative Frequency
Service Time (minutes) Relative Frequency
(a) Using Excel set up a simulation model to simulate about 2 hours (120 minutes) from time zero, and determine whether one attendant is sufficient or whether it is profitable to place a second attendant in the toolshop.
(b) Provide the costs over the 2 hours for the toolmakers’ lost time and for the attendant`s wages.
Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show row and column numbers and be copied from Excel into Word. See Spreadsheet Advice in Interact Resources for guidance.
(c) Your manager has suggested that a reorganisation of the toolshop could reduce the time taken to serve the toolmakers by 2 minutes, ranging from 3 to 7 minutes per toolmaker (but with the same relative frequencies as in parts (a) and (b)). Change the data for service times in your model (copy the model to make the changes, keeping the original model intact). Write a report to your manager explaining your conclusions, suggesting how much might be spent on the reorganisation and still be as well off.
The report must be dated, addressed to the Manager and signed off by you.
(Word limit: No more than 200 words)
QUESTION 4 Regression Analysis and Cost Estimation
20 marks - 4 for (a), 12 for (b), 4 for (c)
Charles Hospital has recorded the following Administrative Costs and two possible cost drivers over the last year.
Administrative Costs ($) Patient Load (Number) Emergency Procedures (Number)
13,900 1,400 10
7,000 500 11
6,000 400 5
10,000 1,000 10
11,900 1,300 12
9,200 900 14
10,200 1,100 8
4,100 300 7
9,400 700 12
11,100 1,200 12
8,300 600 8
16,100 1,500 16
(a) Using the High-Low method of cost estimation and Patient Load as the cost driver, what would be the resulting cost equation for Administrative Costs?
(b) Using Excel, perform three regression analyses to regress Administrative Costs against Patient Load, then against number of Emergency Procedures, then against both of them simultaneously. Paste your results into Word. 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 Patient Load were adopted, what would be the predicted overhead in a month when there were 1,000 Patients and 10 Emergency Procedures?
QUESTION 5 CVP Analysis
20 marks - 4 for (a), 4 for (b), 4 for (c), 8 for (d)
A bicycle manufacturer makes two types of 21-speed bicycles, Road Bikes and Track Bikes. He has sales staff who sell the bikes on commission. The following data are available:
Product Sales Price Variable Production Cost Sales Commission
Road bikes $500 $275 $25
Track bikes $300 $125 $15
Fixed costs per annum are $65,000.
(a) Calculate the unit contribution margin for each product.
(b) This year the manufacturer will specialise in making only Road bikes. How many does he need to sell to break even?
(c) If Road bikes are still the only product what is the breakeven sales volume for the year in sales dollars?
(d) He now decides to manufacture both bikes this year in the ratio of 3 track bikes to 1 road bike.
(i) How many of each bike must be sold to earn a profit of $88,000 before tax for the year?
(ii) How many of each bike must be sold to earn a profit of $105,000 after tax (of 30c in the dollar) for the year?