Question $1$

Consider a client who wants to invest R$800000$

in three types of funds:

A: savings account paying $5\%$ interest per year

$($low risk investment$)$;

B: money$-$market account yielding $7,5\%$ per

year $($medium risk investment$)$; $B$

C: stock market portfolio yielding $10\%$ per year

$($high risk investment$).$

The client requests that the risk distribution

between the medium $(B)$ and high risk $($C$)$

funds must be $2$:$1.$

Suppose the total annual yield was R$50000.$

Compile three independent linear equations

from the data. Convert the equations into a $33$

augmented matrix. Reduce the matrix to

echelon form and determine the amounts

which have been invested in each fund.

Equations?