Problems$*$

$4\mathrm{.}1$ The following gives the number of pints of type A blood used at Woodlawn Hospital in the past $6$ weeks:

$\backslash$table$[[$Week Of$,$Pints Used$],[$August $31,360],[$September $7,389],[$September $14,410],[$September $21,381],[$September $28,368],[$October $5,374]]$

a$)$ Forecast the demand for the week of October $12$ using a $3-$week moving average.

b$)$ Use a $3-$week weighted moving average, with weights of $\mathrm{.}1,\mathrm{.}3,$ and $\mathrm{.}6,$ using $.6$ for the most recent week. Forecast demand for the week of October $12.$

c$)$ Compute the forecast for the week of October $12$ using exponential smoothing with a forecast for August $31$ of $360$ and $=\mathrm{.}2.$