# 39 210 18 6 9 16 5 10 6 10 16 6 13 310 211 19 6 10 16

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[(3*9) + (2*10) + (1*8)] / 6 = 9 1/6 5 10 [(3*11) + (2*9) + (1*10)] / 6 = 10 1/6 6 13 [(3*10) + (2*11) + (1*9)] / 6 = 10 1/6 7 - [(3*13) + (2*10) + (1*11)] / 6 = 11 2/3 Problem 3: 1 1 1 ( ) 500 0.1(450 500) 495 units t t t t F F A F α = + = + =

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7 Problem 4: Month Actual Battery Sales Rounded Forecast for α =0.8 Absolute Deviation for α =0.8 Rounded Forecast for α =0.5 Absolute Deviation for α =0.5 January 20 22 2 22 2 February 21 20 1 21 0 March 15 21 6 21 6 April 14 16 2 18 4 May 13 14 1 16 3 June 16 13 3 14.5 1.5 = 15 = 16 2.56 2.67 On the basis of this analysis, a smoothing constant of α = 0.8 is preferred to that of α = 0.5 because it has a smaller MAD.
8 Problem 5: Year Time Period (X) Sales (Units) (Y) X 2 XY 1996 1 100 1 100 1997 2 110 4 220 1998 3 122 9 366 1999 4 130 16 520 2000 5 139 25 695 2001 6 152 36 912 2002 7 164 49 1148 X = 28 Y =917 X 2 =140 XY = 3961 28 4 7 x x n = = = 917 131 7 y y n = = = 2 2 2 3961 (7)(4)(131) 293 10.46 140 (7)(4 ) 28 xy nxy b x nx = = = = 131 (10.46*4) 89.16 a y bx = = = Therefore, the least squares trend equation is: ˆ 89.16 10.46 y a bx x = + = + To project demand in 2003, we denote the year 2003 as x = 8, and: Sales in 2003 89.16 10.46*8 172.84 = + =

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9 Problem 6: Year Forecast Demand Actual Demand Error RSFE 1 78 71 -7 -7 2 75 80 5 -2 3 83 101 18 16 4 84 84 0 16 5 88 60 -28 -12 6 85 73 -12 -24 MAD = Forecast errors n = = 70 6 117 .
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