$.$ The old deseasonalized forecast is $100$ units, a $=30,$ and the actual demand for the last month was $180$ units. If the seasonal index for the last month is $1\mathrm{.}2$ and the next month is $0\mathrm{.}8,$ calculate:

a$.$ The deseasonalized actual demand for the last month.

b$.$ The deseasonalized forecast for next month using exponential smoothing. c$.$ The forecast of actual demand for the next month