$($THIS IS A LINEAR ALGEBRA QUESTION$)$

In a decentralized finance $($DeFi$)$ ecosystem, three types of cryptocurrencies, Crypto $A,$ Crypto B$,$ and Crypto C$,$ are being traded on a platform. Investors are interested in diversifying their portfolios between these three cryptocurrencies to maximize their potential returns. The current exchange rates and investment constraints are as follows:

$1$ unit of Crypto $A$ is equivalent to $$50.$

$1$ unit of Crypto $B$ is equivalent to $$100.$

$1$ unit of Crypto $C$ is equivalent to $$75.$