Actual sales of a product are given as follows:
Period            1         2        3        4        5        6        7        8        9       10        11        12                              

Actual sales      48       51      54      50      48      47      49      50       52      50       53        54  

Forecast for the first period is 51. Assume smoothing constant   = 0.4 and trend smoothing constant        

i) Forecast by exponential smoothing for each of the periods from 2 onwards. 

ii) Forecast by exponential smoothing including trend adjustment for the same periods.  

iii) Plot the actual sales given and identify the trend in the demand data. 

iv) Plot the forecasted sales in i) and ii), and check which one is closer to the actual ones overall.