HawksBreeze Inc. $($HBI$)$ manufactures air purifiers and needs your assistance predicting the demand for its most popular model. In the table below, you will find the actual demand data from the last $5$ months.

Rounding instructions:

Carry all calculations to at least three decimal places.

Enter all forecasts rounded to the nearest tenth $($one decimal place$).$

Enter MAPE as a percentage rounded to the nearest hundredth of a percent $($e$.$g$.0\mathrm{.}11746$ should be entered as $11\mathrm{.}75\%).$

a$.$ In the past HBI has relied on two qualitative approaches for its forecasting: $1)$ Survey of its sales force; and $2)$ Executives' opinion. Over the past $5$ months, the mean absoulte percent error $($MAPE$)$ for the forecast from executives has been $19\%.$ The forecast based on sales force projections is provided below. Compute the MAPE for this forecast and determine which of the two forecasts has performed better over the past $5$ months.

Month Actual Demand Sales Force Forecast

$1530431$

$2660832$

$3718716$

$4722922$

$5744695$

MAPE for Forecast based on Sales Force Projections: Numeric Response $1.$Edit Unavailable. not attempted, incorrect.$\%$

Which forecast performs better according to the MAPE? $($Award any ties to the Sales Force$)$ Not attempted.

b$.$ Going forward HBI would like to rely on a more quantitative approach using time series methods. Compute an exponential smoothing forecast for Month $6$ with $\backslash$alpha $=0\mathrm{.}8$

F$6=$ Numeric Response $2.$Edit Unavailable. not attempted, incorrect.units.

c$.$ Compute a weighted moving average $($WMA$)$ forecast for Month $6$ with weights of wt$-1=0\mathrm{.}1$ and wt $=0\mathrm{.}9.$

F$6=$ Numeric Response $3.$Edit Unavailable. not attempted, incorrect.units.

d$.$ One key executive would like for you to incorporate trend into your forecast by applying a double exponential smoothing approach starting in Month $5.$ The executive asks you to use values of $\backslash$alpha $=0\mathrm{.}8,\backslash$beta $=0\mathrm{.}3$ and start with initial estimates for Period $4$ of S$4=640$ and T$4=60.$ Complete the table to enter the correct double exponential smoothing forecast.

Period Actual Demand

St

Tt

Dbl$.$ Exp. Smoothing Forecast

$\backslash$alpha $=0\mathrm{.}8,\backslash$beta $=0\mathrm{.}3$

$472264060$

$5744$ Numeric Response $4.$Edit Unavailable. not attempted, incorrect. Numeric Response $5.$Edit Unavailable. not attempted, incorrect. Numeric Response $6.$Edit Unavailable. not attempted, incorrect.

$6$ Numeric Response $7.$Edit Unavailable. not attempted, incorrect.