### Instruction: A math student is tasked with selecting an optimal portfolio with a maximum expected return of 12% for a maximum risk of 10%. After analyzing the market, the student has identified four investment options with expected returns and risks as follows:

- Investment A: Expected return = 9%, Risk = 3%
- Investment B: Expected return = 12%, Risk = 6%
- Investment C: Expected return = 15%, Risk = 9%
- Investment D: Expected return = 18%, Risk = 12%

Which combination of investments will the math student select to form an optimal portfolio? What will be the expected return and risk of the optimal portfolio?### Response: To form an optimal portfolio, the student should consider the investments that provide the highest expected return for a given level of risk, without exceeding the maximum risk of 10%. Let's analyze the possible combinations of investments:

1. A + B: Expected return = (9% + 12%) / 2 = 10.5%, Risk = (3% + 6%) / 2 = 4.5%
2. A + C: Expected return = (9% + 15%) / 2 = 12%, Risk = (3% + 9%) / 2 = 6%
3. A + D: Expected return = (9% + 18%) / 2 = 13.5%, Risk = (3% + 12%) / 2 = 7.5%
4. B + C: Expected return = (12% + 15%) / 2 = 13.5%, Risk = (6% + 9%) / 2 = 7.5%
5. B + D: Expected return = (12% + 18%) / 2 = 15%, Risk = (6% + 12%) / 2 = 9%
6. C + D: Expected return = (15% + 18%) / 2 = 16.5%, Risk = (9% + 12%) / 2 = 10.5%

From the above combinations, we can see that the combination of Investment A and Investment C (A + C) provides an expected return of 12% and a risk of 6%, which meets the student's requirements of a maximum expected return of 12% and a maximum risk of 10%. 

Therefore, the math student should select the combination of Investment A and Investment C to form an optimal portfolio. The expected return of the optimal portfolio is 12%, and the risk is 6%.