A person has \( \$ 30,000 \) to invest. As the person's financial consultant, you recommend that the money be invested in Treasury bills that yield \( 4 \% \), Treasury bonds that yield \( 8 \% \), and corporate bonds that yield \( 12 \% \). The person wants to have an annual income of \( \$ 2200 \), and the amount invested in corporate bonds must be half that invested in Treasury bills. Find the amount in each investment. What is the solution? Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The amount in treasury bills is \( \$ \), the amount in treasury bonds is \( \$ \), and the amount in corporate bonds is \( \$ \). Thpe 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 \( \$ 2 \), where \( z \) is any real number. (Simplify your answers.) C. There is no solution.

Let’s denote the amount invested in Treasury bills as \( x \), in Treasury bonds as \( y \), and in corporate bonds as \( z \). The equations representing the scenario can be derived as follows: 1. Total investment: \[ x + y + z = 30000 \] 2. Income from the investments: \[ 0.04x + 0.08y + 0.12z = 2200 \] 3. Investment relation: \[ z = \frac{1}{2}x \] Now, substituting equation 3 into equations 1 and 2: 1. Replacing \( z \): \[ x + y + \frac{1}{2}x = 30000 \quad \Rightarrow \quad \frac{3}{2}x + y = 30000 \] \[ y = 30000 - \frac{3}{2}x \] 2. For the income: \[ 0.04x + 0.08y + 0.12 \left(\frac{1}{2}x\right) = 2200 \] \[ 0.04x + 0.08(30000 - \frac{3}{2}x) + 0.06x = 2200 \] \[ 0.04x + 2400 - 0.12x + 0.06x = 2200 \quad \Rightarrow \quad -0.02x + 2400 = 2200 \] \[ -0.02x = -200 \quad \Rightarrow \quad x = 10000 \] Now substituting \( x = 10000 \) back to find \( y \) and \( z \): - \( z = \frac{1}{2}(10000) = 5000 \) - \( y = 30000 - \frac{3}{2}(10000) = 30000 - 15000 = 15000 \) So the investments are: 1. Treasury bills: \( \$ 10000 \) 2. Treasury bonds: \( \$ 15000 \) 3. Corporate bonds: \( \$ 5000 \) Thus, the correct choice is: A. There is one solution. The amount in treasury bills is \( \$ 10,000 \), the amount in treasury bonds is \( \$ 15,000 \), and the amount in corporate bonds is \( \$ 5,000 \).