TUTORIAL I TIME SERIES1.Consider the monthly sales data given in Table 1.2.MonthSales(in thousands)a)b)c)d)These are monthly sales (in thousands of dollars) for a one-year period. Sales forecastsfor the next several months are needed in order to plan for raw material purchases,factory labour and plant equipment utilization and financial projections. The simplestforecasts based on past data would be to calculate the average monthly sales and usthat average value ($1243.33) as a forecast for future months. However, as time passesand new data is obtained each month, ideally one would like to update that average.Finde)a)Jan Feb Mar Apr May Jun Jul Aug Sep Octb)c)1212 1321 1278 1341 1257 1287 1189 1111 1145 1150 1298 1331Consider the following data representing monthly retail sales of men's shirts:MonthSales(in thousands)Nov DecThree-month moving average starting with April.Four-month moving average starting with May.Three-month weighted moving average with the weighted value 0.25, 0.3, and0.45.Use exponential smoothing with smoothing parameter of 0.4 to compute thesales forecast.Compute the mean absolute deviation starting from June and for eachof the methods used. Which method would you use to forecast the sales?Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec328 337 341 367 385 403 389 376 428 305 278 450Calculate a three-month moving average forecast. What is your forecast forthe month of January for the following year?Use exponential smoothing with smoothing factor of 0.2 to calculate theforecast for January next year.Compute the mean absolute deviation starting from July and for eachof the methods used. Which method would you use to forecast the sales? TUTORIAL I DECISION ANALYSIS1.2.Even though independent gasoline stations have been having a difficult time, SusanSolomon has been thinking about starting her own independent gasoline station.Susan's problem is to decide how large her station should be. The annual returns willdepend on both the size of her station and a number of marketing factors related to theoil industry and demand for gasoline. After a careful analysis, Susan developed thefollowing table:Size of FirstStationSmallMediumLargeExtra Largecld)e)f)Stock MarketGood Market(S)BondsCDsDecision AlternativeProbabilitya)b)50,00080,000100,000300,000Fair Market(S)For example, if Susan constructs a small station and the market is good, she will realizea profit of $50,000.a)Develop decision table for this decision.b)What is the maximax decision?What is the maximin decision?What is the equally likely decision?what is the criterion of realism decision? Use an a value of 0.8.Develop an opportunity loss table?What is the minimax regret decision?80,00020,00030,00030,000Mickey Lawson is considering investing some money that he inherited. The followingpayoff table gives the profits that would be realized during the next year for each ofthree investment alternatives Mickey is considering:23,0000.530,00025,000Good EconomyPoor Market(S)State of Nature-10,000-20,000-40,000-160,000Poor Economy-20,00020,00023,0000.5What decision would maximize expected profits?What is the maximum amount that should be paid for a perfect forecast ofthe economy?

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