A second version of the Markowitz portfolio model maximizes expected return subject to a constraint that the variance of the portfolio must be less than or equal to some specified amount. Consider the Hauck Financial Service data.

Annual Return $(\%)$

Mutual Fund Year $1$ Year $2$ Year $3$ Year $4$ Year $5$

Foreign Stock $10\mathrm{.}0613\mathrm{.}1213\mathrm{.}4745\mathrm{.}42-21\mathrm{.}93$

Intermediate$-$Term Bond $17\mathrm{.}643\mathrm{.}257\mathrm{.}51-1\mathrm{.}337\mathrm{.}36$

Large$-$Cap Growth $32\mathrm{.}4118\mathrm{.}7133\mathrm{.}2841\mathrm{.}46-23\mathrm{.}26$

Large$-$Cap Value $32\mathrm{.}3620\mathrm{.}6112\mathrm{.}937\mathrm{.}06-5\mathrm{.}37$

Small$-$Cap Growth $33\mathrm{.}4419\mathrm{.}403\mathrm{.}8558\mathrm{.}68-9\mathrm{.}02$

Small$-$Cap Value $24\mathrm{.}5625\mathrm{.}32-6\mathrm{.}705\mathrm{.}4317\mathrm{.}31$

Construct this version of the Markowitz model for a maximum variance of $36.$

Let:

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

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

LG $=$ proportion of portfolio invested in the large$-$cap growth fund

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

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

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

$=$ the expected return of the portfolio

Rs $=$ the return of the portfolio in years

If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a $+$ sign before the blank $($Example: $-300).$ If the constant is $"1"$ it must be entered in the box. If your answer is zero enter $0.$

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

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

FS$\%?$

IB $\%?$

LG$\%?$

LV$\%?$

SG $\%?$

SV $\%?$

Portfolio Expected Return $=\%?$