A portfolio manager is considering investing in three stocks: A, B, and C. The expected returns and standard deviations for the three stocks are as follows:

Stock A: expected return of 10% and standard deviation of 20%
Stock B: expected return of 15% and standard deviation of 25%
Stock C: expected return of 12% and standard deviation of 18%

The correlation coefficients between the stocks are as follows:
Correlation coefficient between A and B is 0.5
Correlation coefficient between A and C is -0.2
Correlation coefficient between B and C is 0.7

If the portfolio manager wants to minimize the portfolio's risk while achieving an expected return of at least 12%, what is the optimal portfolio allocation for each stock?

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