Linear Algebra Homework Word Problem fill in the table and s

Linear Algebra Homework: Word Problem fill in the table and set up equations.

A retired couple wishes to have an additional annual income of $5000 per year. As their financial consultant, you recommend that they invest some money in Treasury Bills that yield %5, some in corporate paper yielding 6%, some in corporate bonds that yield 8% and some in junk bonds that yield 12%. Suppose the couple have $50000 to invest. Set up and solve a system of equations for this problem. Note any natural constraints on the variables. Copy and fill in the table below to show various ways their goal can be achieved.

Solution

Solution:-If the couple invest in T-Bills completely, they will get, 50000X5%=$2500 as annual income

If they invest the amount completely on corporate paper, then they will get, 50,000X6%= $3000 as annual income

It they invest the amount completely on corporate bonds they,witl get, 50,000X8%=$4,000 as an annual income.

If they invest completely, on junk bonds, They will get, 50,000X12%=$6000 AS AN ANNUAL INCOME.

If the couple invest completely on junk bonds, their annual income is more than 5000.But junk bonds are risky, so better to opt for Treasury bills and corporate paper and corporate bonds.

Let x be the amount invested in Treasury bills, y be the amount invested in corporate paer, and z be the amount invested in corporate bonds.

then., 5x+6y+8z =50000 and x+y+z=5000,leaving the junk bonds ,as they are risky.

consider z=1, then, the values of x and y if you solve the equations is the amount that you have to invest for t-bills and corporate paper respectively.