$\backslash$table$[[$Stock $($x$\_($i$)),$Annual Return $($r$\_($i$)),$Variance $($s$\_($i$)^(2))],[1.$ Altacam,$\mathrm{.}08,\mathrm{.}009],[2.$ Bestco,$\mathrm{.}09,\mathrm{.}015],[3.$ Com.com,$\mathrm{.}16,\mathrm{.}040],[4.$ Delphi,$\mathrm{.}12,\mathrm{.}023]]$

$\backslash$table$[[$Stock Combination $($i$,$j$),$Covariances $($r$\_($ij$))],[$A$,$B$,\mathrm{.}4],[$A$,$C$,\mathrm{.}3],[$A$,$D$,\mathrm{.}6],[$B$,$C$,\mathrm{.}2],[$B$,$D$,\mathrm{.}7],[$C$,$D$,\mathrm{.}4]]$Solve the problem stated below and submit the following items:

I. Submit a pdf showing your objective function, constraint and the final solution.

II$.$ Submit the Excel file you constructed for solving this problem.

Minimize

$S=x_1^2{s}_1^2+x_2^2{s}_2^2+$dots$+x_n^2{s}_n^2+{\displaystyle \underset{ij}{\overset{?}{}}}{x}_i{x}_j{r}_{ij}{s}_i{s}_j$

where:

$S=$ variance of annual return of the portfolio

$x_i,x_j=$ the proportion of money invested in investments $i$ or $j$

$s_i^2=$ the variance for investment $i$

$r_{ij}=$ the correlation between returns on investments i and $j$

$s_i,s_j=$ the std$.$ dev. of returns for investments i and $j$

ubject to:

$r_i{x}_i+r_2{x}_2+$dots$+r_n{x}_n{r}_m$

$x_1+x_2+$dots$+x_n=1\mathrm{.}0$

vhere:

$r_i=$ expected annual return on investment $i$

$r_m=$ the minimum desired annual return from the portfolio $=0\mathrm{.}11$