MGMT 2012- Introduction to Quantitative MethodsIndividual Assignment -Graded Assignment Two S2- 2016-17- Due April 15th - 10 percent Final Grade Students should note that this assignment should submitted in a Word document. Question 1A Assume the following payoffs are profits . Payoffs states of nature Decision 1 alternatives A 50 B 35 C 45 2 3 75 55 40 30 60 50 (a) Which alternative should the firm choose under the maximax criterion? (1 mark) (b) Which option should the firm choose under the maximin criterion? (c) Which option should the firm choose under the LaPlace criterion? (2 marks) (d) Which option should the firm choose with the Hurwicz criterion with = 0.4? (2 marks) (e) Using a minimax regret approach, what alternative should the firm choose? (4 marks) (f) Probabilities of 0.25, 0.35, and 0.40 have been assigned. Using expected monetary (1 mark) values, what option should be chosen and what is that optimal expected value? (4 marks) (g) What is the most that the firm should be willing to pay for additional information? Use Expected Regret (3 marks) (h) Use the alternative method to verify EVPI (3 marks) Question 1B Assume now that the pay offs are costs answer the following: (a) (b) (c) (d) (e) (f) g) Using an optimistic approach (maximax), which option would you choose? 1 mark Using a pessimistic approach (maximin), which option would you choose?1 mark If you are a LaPlace decision maker, which option would you choose? 2 marks If you are a Hurwicz decision maker, which option would you choose with = 0.4?1 mark Using a minimax regret approach, which option would you choose? 4 marks Using the same probabilities of 0.25, 0.35, and 0.40 for possible states of nature respectively, which decision alternative will minimise the expected costs? What are the expected annual costs associated with that recommendation? 4 marks What is the most the firm should be willing to pay to obtain further (perfect) information (EVPI)? 3 marks h) Use the alternative method to verify EVPI (3 marks Question 2 A farmer in the Blue Mountains area of Jamaica wants to decide on the crop to plant next season. He wants to plant either ganja or coffee for export to the USA but need some help. He knows that if he plants ganja and the weather in the USA is predominantly cold he earns $10,000(US per month. If the weather is warm he earns $16,000. If he plants coffee and the weather is cold he earns 13,000 and if the weather is warm he earns $14000. In 40% of the years, the weather was cold and in 60 % the weather was warm. For $600, he could buy an expert weather forecast from CWD consulting. States of Nature with Profits ($) Does not include forecast cost Decision Alternatives Warm weather(W) Cold weather (C) Ganja $16,000 $10,000 Coffee $14,000 $13000 Prior Probabilities P(W) = 0.60 P(C) = .40 Conditional probability for a given state of nature where forecasts are either Good (G) or bad (B): That is: P (G|W) = 0.80; P (B|W) = 0.20; P (G|C) = 0.10; P (B|C) = 0.90 After you have computed the revised probabilities round to two decimal places a) Construct the appropriate decision tree to help the farmer make the appropriate decisions. This tree must be constructed in logical order with labels and net payoffs (5 marks). It also includes the revised probabilities (5 marks) (10 marks) b) Fold back the decision tree (5 marks) to determine the best strategy for the farmer; you must state this strategy (1 mark). What is the final expected profit?( 1 mark)(7 marks) c) What is the expected value of sample information(EVSI)- the most that should be paid to seismic testing firm for the test?( 1 mark) d) Calculate the expected value of perfect information (EVPI)- the most that should be paid CWD for prediction of the uncertain outcomes.(1 mark) e) What is the efficiency of sample information?(1 mark) Question 3 Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply are shown in the following table. a)Estimate demand with a weighted moving average in which sales in the most recent year, next most recent , most distant are given weights of 3,2 and 1 respectively . Compute the MAD, MSE and MPE for this method.( six marks) b)Use exponential smoothing with a smoothing constant of 0.2 to forecast the demand for fertilizer. Assume that last period's forecast for year 1 is 5,000 bags to begin the procedure. Which method do you think is best?. Is this an improvement over the weighted average- use MAD alone( Six marks) c) Use regression analysis to estimate the line of best fit( eight marks). Forecast the demand for years 12 and 13. Question four A new project is to be completed. The following activities need to be completed in the order shown, where times are in weeks. Activity Immediate Optimistic Most Most Variance predecessors time likely pessimistic time time A B C D E F G H I J A,B B A C E,F D,F G,H I 2 2 1 1 2 1 2 2 1 2 3 4 2 3 3 4 2 5 3 3 4 6 3 5 4 7 2 8 5 4 0.11111 0.44444 0.11111 0.44444 0.11111 1 0 1 0.44444 0.11111 You must use two decimal places at all times for expected times when they are not integer (you are not permitted to round off to integers). (a) (b) (c) (d) (e) (f) Draw the activity network for this problem (6 marks) Determine the Expected Times. (1 mark) Determine the activity schedule (ES, EF, LS, and LF) as well as slack. (7 marks) Determine and state the critical path for this project. (1 mark) What are the expected time and the variance of the project? (2 marks) What is the probability that the project is completed in 22 or fewer weeks(1 mark) (g) What date should be set such that there is a 94% chance of completion within that time? (2 marks)