A financial institution offers three types of investment products: Savings Account, Fixed Deposit, and Mutual Fund. The institution has determined the interest rates and investment limits for each product as follows:Savings Account: Interest rate $=2\%$ per annum, maximum investment $=$ $$10,000$Fixed Deposit: Interest rate $=5\%$ per annum, maximum investment $=$ $$50,000$Mutual Fund: Interest rate $=8\%$ per annum, maximum investment $=$ $$100,000$ The institution aims to maximize its interest income while adhering to the following constraints:The total investment in Savings Accounts should not exceed $$30,000.$The total investment in Fixed Deposits should not exceed $$80,000.$The total investment in Mutual Funds should not exceed $$150,000.$Let x$,$ y$,$ and z represent the amounts invested in Savings Account, Fixed Deposit, and Mutual Fund respectively.$($a$)$ Formulate a system of linear equations representing the investment constraints described above.Solve the system of equations using matrix algebra to determine the optimal investment amounts for Savings Account, Fixed Deposit, and Mutual Fund.$($d$)$ Interpret your results in the context of the financial institution's investment strategy.