Sales for the past $8$ months at Dalworth Company are given here.

Month Sales $($$ Millions$)$

Jan $20$

Feb $24$

Mar $27$

Apr $31$

May $37$

Jun $47$

July $53$

August $62$

a$)$ Use a $3-$month weighted moving average to forecast the sales for the months June, July, and

August. Use weights of $(10),(5),$ and $(1),$ giving more weight to more recent data. $(6\mathrm{.}5$ pts$)$

b$)$ Use exponential smoothing with $=0\mathrm{.}4$ to forecast the sales for the months June, July, and

August. Assume that the forecast for May was $$39$ million. $(6\mathrm{.}5$ pts$)$

c$)$ Calculate the Mean Absolute Percent Error $($MAPE$)$ for each of the two forecasting methods: $3-$

month weighted moving average and exponential smoothing, for each month $($June$,$ July, and

August$).$ Based on these calculations, identify which method provided a more accurate forecast

for each month. Be sure to show all error measurements. $(7$ pts$)$