The number of items sold over a four-month period are: month 1 2 3 4 sales 5100 5500 5400 5600 Calculate the forecasts for the 4th and 5th months using 3-month weighted moving average method with weights of 0.6 for the most recent month and 0.3 for the next to the most recent month. Further, suppose that the exponential smoothing constant α=0.5. Then calculate the forecasts for 3rd, 4th and 5th months, using exponential smoothing method. Under the 3-month weighted moving average method, what is the forecast for the fourth month?

By using 3-month weighted moving average method -

Forecasts for the 4th month = 5400

Forecasts for the 5th month = 5530

By using Exponential smoothing method -

Forecasts for 3rd month = 5300

Forecast for 4th month = 5350

Forecast for  5th month = 5475

Step-by-step explanation:

To find - Calculate the forecasts for the 4th and 5th months using 3-month weighted moving average method.

Calculate the forecasts for 3rd, 4th and 5th months, using exponential smoothing method.

Proof -

Given that,

month           1            2              3              4

sales         5100       5500     5400        5600

F(4) = 0.6 A(3) + 0.3 A(2) + 0.1 A(1)

      = 0.6 [ 5400] + 0.3 [ 5500] + 0.1 [ 5100]

      = 3240 + 1650 + 510

      = 5400

⇒forecasts for the 4th month = 5400

Now,

F(5) = 0.6 A(4) + 0.3 A(3) + 0.1 A(2)

      = 0.6 [ 5600] + 0.3 [ 5400] + 0.1 [ 5500]

      = 3360 + 1620 + 550

      = 5530

⇒forecasts for the 5th month = 5530

Now,

Given that, the exponential smoothing constant α=0.5

Month                   Sales                           Forecast

1                             5100                            5100

2                            5500                           5100 + 0.5(5100 - 5100) = 5100

3                             5400                          5100 + 0.5(5500 - 5100) = 5300

4                             5600                          5300 + 0.5(5400 - 5300) = 5350

5                                                                 5350 + 0.5(5600 - 5350) = 5475

∴ we get

By using Exponential smoothing method -

Forecasts for 3rd month = 5300

Forecast for 4th month = 5350

Forecast for  5th month = 5475

good luck on your studies! : )

david edward.

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a