The following table gives the number of pints of type A blood used at Damascus Hospital in the past $6$ weeks:

$\backslash$table$[[$Week Of$,$Pints Used$],[$August $31,360],[$September $7,389],[$September $14,412],[$September $21,383],[$September $28,371],[$October $5,374]]$

a$)$ The forecasted demand for the week of October $12$ using a $3-$week moving average $=376\mathrm{.}00$ pints $($round your response to two decimal places$).$

b$)$ Using a $3-$week weighted moving average, with weights of $0\mathrm{.}15,0\mathrm{.}30,$ and $0\mathrm{.}55,$ using $0\mathrm{.}55$ for the most recent week, the forecasted demand for the week of October $12=374\mathrm{.}45$ pints $($round your response to two decimal places and remember to use the weights in appropriate order $-$ the largest weight applies to most recent period and smallest weight applies to oldest period.$)$

c$)$ If the forecasted demand for the week of August $31$ is $360$ and $=0\mathrm{.}25,$ using exponential smoothing, develop the forecast for each of the weeks with the known demand and the forecast for the week of October $12($round your responses to two decimal places$).$

$\backslash$table$[[$Week Of$,$Pints Used,$\backslash$table$[[$Forecast for this$],[$Date$]]],[$August $31,360,360],[$September $7,389,360\mathrm{.}00],[$September $14,412,367\mathrm{.}25],[$September $21,383,378\mathrm{.}44],[$September $28,371,379\mathrm{.}58],[$October $5,374,377\mathrm{.}44],[$October $12,-,376\mathrm{.}58]]$