National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a s
ID: 422014 • Letter: N
Question
National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a seven-month period were as follows Sales Month(000)Units Feb Mar. Apr May Jun. Jul Aug 19 18 15 20 18 20 b. Forecast September sales volume using each of the following (1) A linear trend equation. (Round your intermediate calculations and final answer to 2 decimal places.) thousands (2) A five-month moving average Moving average thousands (3) Exponential smoothing with a smoothing constant equal to .20, assuming a March forecast of 19(000). (Round your intermediate calculations and final answer to 2 decimal places.) Forecast thousands (4) The naive approach. Naive approach thousands (5) A weighted average using .60 for August, .30 for July, and .1O for June. (Round your answer to 2 decimal places.) Weighted averagee thousandsExplanation / Answer
Answer to question 1 :
Let the linear trend equation :
Y = a + b.t
Y = Sales in ‘000 units
T = Serial number of month ( Feb = 1 , Mar = 2 , April = 3 …. August =7 , September = 8 )
A, b = Constants
We place all the values of month ( in numbers ) and sales (‘000 units ) in two parallel columns in excel and apply the formula LINEST ( ) , and obtain following values of a and b :
a = 16.857
b = 0.5
Therefore , Yt = 16.857 + 0.5.t
To determine value for September, we put t = 8 and obtain following value of Y
Y = 16.857 + 0.5 x 8 = 16.857 + 4 = 20.857 ( 20.86 rounded to 2 decimal places )
Yt = 20.86 THOUSANDS
Answer to question 2 :
Forecast for September basis 5 month moving average
= Sum of sales value from April to August / 5
= ( 15 + 20 + 18 + 22 + 20 ) / 5
= 95/5
= 19
MOVING AVERAGE = 19 THOUSANDS
Answer to question 3 :
Following will be the formula for exponential smoothing forecast :
Ft = alpha x At-1 + ( 1 – alpha) x Ft-1 = 0.20x at-1 + 0.8 x Ft-1
Ft, Ft-1 = Forecast values for period t and t-1 respectively
At-1 = Actual sales for period t-1
Alpha = exponential smoothing forecast = 0.2
It is given forecast for March = 19 ( in ‘000)
Accordingly forecast for subsequent periods including September in below table :
Month
Actual sales
Forecast sales
Feb
19
March
18
19.00
April
15
18.80
May
20
18.04
June
18
18.43
July
22
18.35
August
20
19.08
September
19.26
FORECAST = 19.26 THOUSANDS
Answer to question 4 :
As per Naïve approach ,
Forecast for period t = Actual sales for period t-1
Accordingly,
Forecast for September = Actual sales for August = 20 ( thousands)
FORECAST = 20 THOUSANDS
Answer to question 5 :
Forecast for September ( in thousands )
= 0.60 x Actual sales for august + 0.3 x actual sales for July + 0.10 x actual sales for June
= 0.60 x 20 + 0.3 x 22 + 0.1 x 18
= 12 + 6.6 + 1.8
= 20.4
WEIGHTED AVERAGE = 20.4 THOUSANDS
Yt = 20.86 THOUSANDS
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