Please show all your work for maximum credits.

$1.$ Historic demand for a product is

$$ Month$$ Demand

$$ January$12$

$$ February$11$

$$ March$15$

$$ April $12$

$$ May$16$

$$ June$15$

$$

a$)$ Using a weighted $3-$month moving average with weights of $0\mathrm{.}60,0\mathrm{.}30,$ and $0\mathrm{.}10,$ Find the July forecast. $($Note: the most recent period should be given greater weight$)$

b$)$ Using a simple $3-$month moving average, find the July forecast

c$)$ Using single exponential smoothing with a $=0\mathrm{.}4$ and a June forecast $=14,$ find the July forecast.

$$

$2.$ The following tabulations are actual sales of units for six months and a starting forecast in January.

a$)$ Calculate forecasts for the remaining five months using simple exponential smoothing with a $=0\mathrm{.}3.$

b$)$ Calculate MAD for the forecasts.

$$ Month$$ Actual$$ Forecast

$$ January$10080$

$$ February$98$

$$ March $106$

$$ April$80$

$$ May$68$

$$ June$94$

$$

$$

$3.$ Here are the actual tabulated demands for an item for a nine$-$month period $($January through September$).$ Your supervisor wants to test two forecasting methods to see which method was better over this period

$$ Month$$ Actual$$ Month $$ Actual

$$ January$110$ June$180$

$$ February$130$ July$140$

$$ March$150$ August$150$

$$ April$170$ September$130$

$$ May$160$

$$

a$)$ Forecast April through September using a three$-$month moving average

b$)$ Use a simple exponential smoothing with an alpha of $0\mathrm{.}6$ to estimate demands for May through September. $($assume the forecasted demand for April was $150)$

c$)$ Calculate MAD, MSE, and MAPE for $($a$)$ and $($b$)$

d$)$ Base on your answers in c$),$ which do you think is a better forecasting method?