$1-(12$ points$)$ The following equation summarizes the trend projection of quarterly sales of condos over a long cycle. Sales exhibit seasonal variation. Using the information given, prepare seasoned forecast of sales for each quarter of next year $($not this year$).$

$F_t=40-6\mathrm{.}5t+2t^2,$ where $F_t=$ Unit sales, $t=1$ is $1^{st}$ quarter of last year

Assume seasonal relatives $Q1=1\mathrm{.}1,Q2=1\mathrm{.}0,$ and $Q3=0\mathrm{.}6$

Find Q$4$ seasonal relative: Seasonal relatives adds to the number of seasons;

Q$4=4-(1\mathrm{.}1+1\mathrm{.}0-0\mathrm{.}6)=1\mathrm{.}3$

Q$1$next year $t=9,F_9=40-6\mathrm{.}5(9)+2(9{)}^2=143\mathrm{.}5,$ seasonally adj. $=143\mathrm{.}5**1\mathrm{.}1=157\mathrm{.}85$

Q$2$ next year $t=10,F_{10}=40-6\mathrm{.}5(10)+2(10{)}^2=175\mathrm{.}0,$ seasonally adj. $=175\mathrm{.}0**1\mathrm{.}0=175\mathrm{.}0$

Q$3$ next year $t=11,F_{11}=40-6\mathrm{.}5(11)+2(11{)}^2=210\mathrm{.}5,$ seasonally adj. $=210\mathrm{.}5**0\mathrm{.}6=126\mathrm{.}3$

Q$4$ next year $t=12,F_{12}=40-6\mathrm{.}5(12)+2(12{)}^2=250\mathrm{.}0,$ seasonally adj. $=250\mathrm{.}0**1\mathrm{.}3=325\mathrm{.}0$