The risk on a portfolio made up two assets $($A & B$)$ is given by

$2+0\mathrm{.}542+0\mathrm{.}25$

Where and are the weights $($proportion of capital invested in each asset$)$ for assets

and respectively.

A$)$ Find the weights that would minimize this portfolios risk subject to the constraint that the weights must add up to one. $(7$ marks$)$

B$)$ Check that you indeed have minimized risk. $(8$ marks$)$

C$)$ When presenting a solution, it is crucial to thoroughly examine the many phases involved and their respective objectives. Furthermore, it is advantageous to present a concrete mathematical illustration derived from real$-$world scenarios, when there exists an objective function that necessitates either minimization or maximisation while being subject to certain limitations$.(<500$ words$)(10$ marks$)$