Problem $1.(10$ points$)$

A manager recorded the number of gallons of ice cream sold for the past six 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 simple moving average model, and a three$-$period weighted moving average model with weights of $0\mathrm{.}5,0\mathrm{.}3$ and $0\mathrm{.}2.$

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

b$)$ What is the forecast of demand for period $9,$ considering the best model? $(1$ point$)$

$\backslash$table$[[$Period$,$Demand$],[1,720],[2,900],[3,800],[4,840],[5,700],[6,680],[7,810],[8,760]]$