Consider is the amount invested in treasury bills.

is the amount invested in corporate bonds.

is the amount invested in junk bonds.

The total investment equation is .

Annual income equation is .

Definition of augment matrix :

If  are the system of equations then the augmented matrix is .

Augment matrix of the system of equations is .

Apply .

Apply .

Apply .

Apply .

The matrix in the last step represents the system .

The solution of the system is and .

(a)

The income is .

The solution of the system is and .

Substitute in .

.

Substitute in .

.

Since and cannot be negative, we must have .Investing all of the money at yields , which is more than the needed.

(b)

The income is The solution of the system is and .

Substitute in .

.

Substitute in .

.

Possible investment strategies:

Amount invested at

(c)

The income is .

The solution of the system is and .

Substitute in .

.

.

Substitute in .

.

Possible investment strategies:

Amount invested at

(a) Since and cannot be negative, we must have .

Investing all of the money at yields , which is more than the needed.

(b)

Amount invested at

(c)

Amount invested at