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National Scan, Inc. sells radio frequency inventory tags. Monthly sales for a seven month period were as follows.

Month Sales (000)Units
Feb. 19
Mar. 22
Apr. 8
May 24
Jun 19
Jul 27
Aug 22
b. Forecast September sales volume using each of the following

1. A linear trend equation. Round intermediate calculations and finals answer to 2 decimal places.

YT = _____ thousands

2. A five-month moving average. Round answer to 2 decimal places.

3. Exponential smoothing with a smoothing constant equal to 0.25 assuming a March forecast of 17(000). Round intermediate forecast values and final answer to 2 decimal places.

Forecast _____ thousands

4. The naive approach

Naive approach _____thousands

5. A weighted average using .50 for August .15 for July, and .35 for June. Round your answer to 2 decimal places.

Weighted average _____thousands

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opudodennis

Answer:

[tex]a. 28.70\\b. 20.00\\c.20.73\\d.20.14\\e.21.70[/tex]

*All values are in thousandsHence September forecast is

Explanation:

a. let [tex]x[/tex] represent number of months and [tex]y[/tex] sales

[tex]\sum x=28 \ ,\sum y=141\ , \bar x=4 \ ,\bar y=20.14[/tex]

We then calculate squares, products and totals:

Squares of x: [tex]1,4,9,16,25,36,49[/tex]  and  [tex]\sum x^2=140[/tex]

Squares of [tex]y[/tex]: [tex]361,484,64,576,361,729,484[/tex]  and  [tex]\sum y^2=3059[/tex]

Products of xy: [tex]19,44,24,96,95,162,154[/tex] and  [tex]\sum xy= 594[/tex]

Linear regression is given by the equation [tex]y=bx+c[/tex]

[tex]S_x_x=140-28^2/7=28[/tex]

[tex]S_x_y=594-(141\times28)/7=30[/tex]

[tex]b=30/28=1.07[/tex]

[tex]c=\frac{141}{7}=20.14[/tex]

Linear equation is now given as [tex]y=1.07x+20.14[/tex]

Hence September forecast is calculated as:

[tex]y=1.07(8)+20.14=28.70[/tex]

b. 5-month moving average:

[tex]MA_5=\frac{1}{5}(22+27+19+24+8)=20[/tex]

c.Exponential smoothing given smoothing constant of [tex]0.25[/tex]

Month forecast=[tex]F(Old)-0.25[Actual-F(Old)][/tex]

April=

[tex]17+0.25(22-17)=18.25\\May:18.25+0.25(8-18.25)=15.69\\June:15.69+0.25(24-15.69)=17.77\\July:17.77+0.25(19-17.77)=18.08\\Aug:18.08+0.25(27-18.08)=20.31\\Sep:20.31+0.25(22-20.31)=20.73[/tex]

20.73

d. Naive Approach

[tex]=(\bar x_7 \times 8)-\sum x_7)\\=20.14\times 8-141\\=20.14[/tex]

e.  Weighted Average

[tex]=0.50*22+0.15*27+0.35*19\\=21.7[/tex]

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