$$Part b$.$ This part includes $3$ calculation questions regarding Chapter $4$ Forecasting. Show your steps to earn full credit. Note: You can either type your answer in this word file, or you can print it out, work on it$,$ and scan the file back in$.$ I$\text{'}$m fine with either option, and whatever the option you choose, it should be the second file you turn in for this assignment.

$1.$ As you can see in the following table, demand for heart transplant surgery at Washington General Hospital has increased steadily in the past few years:

The director of medical services predicted $6$ years ago that demand in year $1$ would be $41$ surgeries.

a$)$ Use a $3-$year moving average to forecast demand in years $4,5,$ and $6.$

b$)$ Use a $3-$year weighted moving average, with weights of $\mathrm{.}1,\mathrm{.}3,$ and $\mathrm{.}6,$ using $.6$ for the most recent year. Forecast demand for the year $4,5,$ and $6.$

c$)$ Compute the forecast for the Year $6$ using exponential smoothing with a forecast for Year $1$ is $40$ and $\backslash ($ a$=2\backslash ).$

d$)$ Use the trend$-$projection method to forecast demand in years $1$ through $6.$

e$)$ With MAD as the criterion, which forecasting method is better?

please answer all questions $1$a$-$e$.$ show work.