Problem $1.(10$ points$)$

A manager recorded the number of gallons of ice cream sold for the past eight periods. He asked you to choose a forecasting model to predict the demand for gallons of ice cream in Period $9.$ You consider applying a three$-$period moving average model and a three$-$period weighted moving average model with weights of $0\mathrm{.}40,0\mathrm{.}35$ and $0\mathrm{.}25.$

$\backslash$table$[[$Period$,$Demand$],[1,525],[2,600],[3,450],[4,675],[5,800],[6,750],[7,650],[8,750]]$

a$)$ Which model is better for this data set $($hint: show all your work including forecasts for each period and calculations using measures of forecast accuracy$)?(9$ points$)$

b$)$ What is the forecast of demand for period $9$ when you use the best model for the data? $(1$ point$)$