$\backslash$table$[[,$Annual Return $(\%)],[$Mutual Fund,Year $1$ Year $2,$Year $3$ Year $4$ Year $5,,,],[$Forelgn Stock,$10\mathrm{.}06,13\mathrm{.}12,13\mathrm{.}47,45\mathrm{.}42,-21\mathrm{.}93],[$Intermediate$-$Term Bond,$17\mathrm{.}64,3\mathrm{.}25,7\mathrm{.}51,-1\mathrm{.}33,7\mathrm{.}36],[$Large$-$Cap Growth,$32\mathrm{.}41,18\mathrm{.}71,33\mathrm{.}28,41\mathrm{.}46,-23\mathrm{.}26],[$Large$-$Cap Value,$32\mathrm{.}36,20\mathrm{.}61,12\mathrm{.}93,7\mathrm{.}06,-5\mathrm{.}37],[$Small$-$Cap Growth,$33\mathrm{.}44,19\mathrm{.}40,3\mathrm{.}85,58\mathrm{.}68,-9\mathrm{.}02],[$Small$-$Cap Value,$24\mathrm{.}56,25\mathrm{.}32,-6\mathrm{.}70,5\mathrm{.}43,17\mathrm{.}31]]$

$($a$)$ Construct this version of the Markowitz model for a maximum variance of $32.$

Let:

FS $=$ proportion of portfolio invested in the foreign stock mutual fund

$IB=$ proportion of portfolio invested in the intermedlate$-$term bond fund

$LG=$ proportion of portfollo Invested in the large$-$cap growth fund

$LV=$ proportion of portfollo invested in the large$-$cap value fund

SG a proportion of portfolio invested in the small$-$cap growth fund

$SV=$ proportion of portfollo invested in the small$-$cap value fund

$\frac{?}{\text{b}\text{a}\text{r}}(R)=$ the expected return of the portfolio

$R_s=$ the return of the portfollo in year $s$

$($b$)$ Solve the model developed in part $($a$).$

If required, round your answers to two decimal places. If your answer is zero, enter $"0",$

$\backslash$table$[[FS,30\mathrm{.}3,],[IB,37\mathrm{.}9,\%$