is this correct?Complaints data: February $(15),$ March $(16),$ April $(20),$ May $(22),$ June $(18),$ July $(22),$ August $(22).$

Forecasting methods: $4-$month moving average, exponential smoothing $($smoothing constant $=0\mathrm{.}10),$ weighted average $($weights: Aug $=0\mathrm{.}50,$ July $=0\mathrm{.}30,$

Apply the forecasting methods:

a$)4-$month moving average:

Average of May, June, July, and August: $(22+18+22+22)/4=21.$

Forecast for September: $21.$

b$)$ Exponential smoothing:

Forecast for September: F$($t$)=$ $*$ Y$($t$-1)+(1-$ $)*$ F$($t$-1),$ where is the smoothing constant $(0\mathrm{.}10).$

Initial forecast for August: F$($Aug$)=$ August complaints $=22.$

Forecast for September: F$($Sept$)=0\mathrm{.}10*22+(1-0\mathrm{.}10)*2221\mathrm{.}80.$

c$)$ Weighted average:

Forecast for September: $(0\mathrm{.}50*22)+(0\mathrm{.}30*22)+(0\mathrm{.}20*18)=21\mathrm{.}60.$

June $=0\mathrm{.}20).$

Compare the results:

$4-$month moving average: Forecast for September $=21.$

Exponential smoothing: Forecast for September $21\mathrm{.}80.$

Weighted average: Forecast for September $21\mathrm{.}60.$

Determine the most appropriate method:

Comparing the forecasted values, we find that the $4-$month moving average method provides a forecast of $21,$ which is the closest to the actual number of complaints received in September.

Method

Forecast for September

$4-$month moving average

$21$

Exponential smoothing

$21\mathrm{.}80$

Weighted average

$21\mathrm{.}60$

Based on the given data, the $4-$month moving average method is the most appropriate for forecasting September's complaint volume, with an estimated value of $21.$