Response the following:
1. An investor has a certain amount of money available to invest now. Three alternative investments are available.The estimated profits ($) of each investment under each economic condition are indicated in the following payoff table:...in each part draw a clear conclusion based on your calculations.
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Investment selection
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Economy declines
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No change
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Economy expands
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A...d1
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500
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1000
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2000
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B...d2
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-2000
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2000
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5000
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C...d3
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-7000
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-1000
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20 000
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a) What is the recommended decision using the optimistic approach?
b) What is the recommended decision using the conservative/pessimistic approach?
c) What is the recommended decision using the minimax regret approach?
2. The following payoff table shows profit for a decision analysis problem with four different decision alternatives d1-d4 and three states of nature s1-s3.
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Events 4
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Boom (5,)
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Stagnation DO
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Recession (s3)
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Alternatives/Probabilities
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0.2
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0.5
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0.3
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Expand the business (CI)
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900.000
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300.000
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-400.000
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Maintain the business at current level WO
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400.000
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250.000
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120.000
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Contract the business (c1,)
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-200000
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-50000
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200000
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Contract the business significantly (d4)
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-20000
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50000
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a) What is the recommended decision using the expected value approach?
b) Find the expected value with perfect information.
c) Find expected value of perfect information.
3. The following is a 7-month-demand-history for a certain product.
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Month
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Period (X) Demand (Y)
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January 134
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1
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300
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February
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2
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325
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March
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3
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468
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April
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4
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426
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May
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5
|
621
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June
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6
|
554
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July
|
|
543
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a) Assuming that linear trend appears, develop the equation of regression line. Round values of coefficients to two decimal places.b) Use the equation to prepare a forecast for December 2004.
4. Use graphical sensitivity analysis to determine the range of probabilities for which each of three decision alternative has the largest expected value.The payoffs represent projected profits. Write clear conclusion. Round values of p to 3 decimal places.
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Alternative
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State of Nature
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Favorable
Market ($)
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Unfavorable
Market ($)
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Construct a large plant
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200.000
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-180,000
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Construct a small plant
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100.000
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-20.000
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Do nothing
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0
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0
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5. Alabama building contracts for a 8-month period (in millions of dollars) are 240, 350, 230, 260, 280, 320, 220, 310.
a) Calculate a five-month moving average forecast. Find its MSE (3 decimal places).
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month
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Time series value
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5-month moving average forecast
(2 decimal places)
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Forecast error
(2 decimal places)
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Squared forecast error
(2 decimal places)
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1
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240
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|
|
|
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2
|
350
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|
|
|
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3
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230
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|
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4
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260
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|
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5
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280
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6
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320
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7
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220
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8
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310
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b) Calculate an exponential smoothing forecast using =0.4. Find its MSE.
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month
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Time series value
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Exponential smoothing forecast  =0.4
rounding to 3 places
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Forecast error
rounding to 3 places
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Squared forecast error
rounding to 3 places
|
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1
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240
|
|
|
|
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2
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350
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|
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|
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3
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230
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|
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4
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260
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5
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280
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6
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320
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7
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220
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|
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8
|
310
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|
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c) Using the more accurate method, find the forecast for next month.
6. A large business has fixed costs of £250,000 per week. Its average sales revenue per item is £2, and its variable costs are on average 40p per item.
Note: all of the data must have equal units.
a) What is breakeven point?
b) What profit or loss can be anticipated with a demand of 200 000 units?
c) With a demand of 200 000 copies, what is the minimum price per unit the company must charge to break even?
d) Graph both R(x) and C(x) from part a) into one figure.
7. An author is trying to choose between two publishingcompanies that are competing for the marketing rights to hernew novel. Company A has offered the author $10,000 plus $2 per book sold. Company B has offered the author $2,000plus $4 per book sold. The author believes that five levels of demand for the book are possible: 1,000, 2,000, 5,000,10,000, and 50,000 books sold.
Construct a payoff table, indicating the decision alternatives (Company A and B) and states of nature given by different demands.Payoffs must represent the author's revenue.
8. Only suggest type of the calculation as NPD, PPD, BPD, do not perform any further calculations.
a) It is estimated that one third of the general population has blood type A+. If a sample of 9 people is chosen randomly, what is the probability that exactly three of them have blood type A+?
b) On Saturday mornings, customers enter a boutique at a suburban shopping mall at an average rate of 0.5 per minute. What is the probability that3 customers arrive in a specified 10-minute interval of time.
c) A certain amount of material is wasted in cutting patterns for garments. A producer of army uniforms has found that the wastage is normally distributed with mean 4.1% and standard deviation 0.6%, from lot to lot. What is the probability that the wastage exceeds 5%?
d) In an audit of a company's billings, an auditor randomly selects 5 bills. If 3% of all bills contain an error, what is the probability that the auditor will find 2 bills in error?
9. Circle your answer clearly:
a) Problem solving includes both the identification of a problem and the action to resolve it.
True
False
b) The decision making process includes implementation and evaluation of the decision.
True
False
c) Regression line equation is the example of smoothing forecasting.
True
False
d) Decision criteria
a. are the choices faced by the decision maker.
b. are the problems faced by the decision maker.
c. are the ways to evaluate the choices faced by the decision maker.
d. must be unique for a problem.
e) The volume that results in marginal revenue equaling marginal cost is called the break-even point.
True
False
f) Name four components of time series: