Ten months of data and the forecasts for those same periods are in the table below. Create an exponential smoothing forecast for February onwards, assuming that the January forecast was $42.$ Which value of alpha gives the best forecast using the MAPE criterion?

Month Actual

January $42$

February $58$

March $58$

April $,77$

May $91$

June $,102$

July $,124$

August $148$

September $171$

October $177$

alpha $=0\mathrm{.}4$

alpha $=0\mathrm{.}2$

alpha $=0\mathrm{.}3$