Questions: A person has 40,000 to invest. As the person's financial consultant, you recommend that the money be invested in Treasury bills and corporate bonds. The person wants to have an annual return of 1,040, and the amount invested in corporate bonds must not be less than invested in Treasury bills. Find the amount in each investment. What is the solution? Select the correct choice below and fill in any answers within your choice. A. There is one solution. The amount in treasury bills is 9000, the amount in treasury bonds is 31,000, and the amount in corporate bonds is 0000. (Type integers or decimals.) B. There are infinitely many solutions. The amount in treasury bills is , the amount in treasury bonds is , and the amount in corporate bonds is , where x is any real number. (Simplify your answers.) C. There is no solution.

A person has 40,000 to invest. As the person's financial consultant, you recommend that the money be invested in Treasury bills and corporate bonds. The person wants to have an annual return of 1,040, and the amount invested in corporate bonds must not be less than invested in Treasury bills. Find the amount in each investment.

What is the solution? Select the correct choice below and fill in any answers within your choice.

A. There is one solution. The amount in treasury bills is 9000, the amount in treasury bonds is 31,000, and the amount in corporate bonds is 0000. (Type integers or decimals.)

B. There are infinitely many solutions. The amount in treasury bills is , the amount in treasury bonds is , and the amount in corporate bonds is , where x is any real number. (Simplify your answers.)

C. There is no solution.

Transcript text: A person has $40,000 to invest. As the person's financial consultant, you recommend that the money be invested in Treasury bills and corporate bonds. The person wants to have an annual return of $1,040, and the amount invested in corporate bonds must not be less than invested in Treasury bills. Find the amount in each investment. What is the solution? Select the correct choice below and fill in any answers within your choice. A. There is one solution. The amount in treasury bills is $9000, the amount in treasury bonds is $31,000, and the amount in corporate bonds is $0000. (Type integers or decimals.) B. There are infinitely many solutions. The amount in treasury bills is $, the amount in treasury bonds is $, and the amount in corporate bonds is $, where x is any real number. (Simplify your answers.) C. There is no solution.

Solution

Solution Steps

To solve this problem, we need to set up a system of equations based on the given conditions. Let $ x $ be the amount invested in Treasury bills and $ y $ be the amount invested in corporate bonds. The total investment is $40,000, so $ x + y = 40,000 $. The annual return is $1,040, which can be expressed as a linear combination of the returns from Treasury bills and corporate bonds. Additionally, the amount invested in corporate bonds must not be less than the amount invested in Treasury bills, so $ y \geq x $. We will solve this system of equations to find the values of $ x $ and $ y $.

Step 1: Set Up the Equations

Let $ x $ be the amount invested in Treasury bills and $ y $ be the amount invested in corporate bonds. We have the following equations based on the problem statement:

Total investment: \[ x + y = 40000 \]
Annual return: \[ 0.02x + 0.05y = 1040 \]

Step 2: Solve the System of Equations

We can solve the system of equations to find the values of $ x $ and $ y $. From the first equation, we can express $ y $ in terms of $ x $: \[ y = 40000 - x \]

Substituting this expression for $ y $ into the second equation gives: \[ 0.02x + 0.05(40000 - x) = 1040 \]

Step 3: Simplify and Solve for $ x $

Expanding and simplifying the equation: \[ 0.02x + 2000 - 0.05x = 1040 \] \[ -0.03x + 2000 = 1040 \] \[ -0.03x = 1040 - 2000 \] \[ -0.03x = -960 \] \[ x = \frac{-960}{-0.03} = 32000 \]

Step 4: Calculate $ y $

Now, substituting $ x = 32000 $ back into the equation for $ y $: \[ y = 40000 - 32000 = 8000 \]