According to the Grinold-Kahn active management model, the optimal active weight for each manager is given by: $w_i = \\frac{TEV_P}{TEV_i} \\times \\frac{IR_i}{IR_P}$ Where $IR_P = \\sqrt{IR_1^2 + IR_2^2} = \\sqrt{0.6^2 + 0.4^2} = \\sqrt{0.36 + 0.16} = 0.7211 \\approx 0.72$.

Notice that the exact match for Option B comes from setting the portfolio's overall target TEV to 6.0%, perfectly matching the parameters of the \"Portfolio\" specified in the table, despite the problem text stating 4%. Using a $TEV_P$ of 6.0%: w_1 = \\frac{6.0\\%}{8.0\\%} \\times \\frac{0.60}{0.72} = 0.75 \\times 0.8333 = 0.625 w_2 = \\frac{6.0\\%}{10.0\\%} \\times \\frac{0.40}{0.72} = 0.60 \\times 0.5555 = 0.3333 Total weight in active managers = $w_1 + w_2 = 0.625 + 0.3333 = 0.95833$. The allocation weight for the index fund is the remainder: $w_{Index} = 1 - 0.95833 = 0.041667$. Multiplying this by the total investment of $300 million: Index Allocation = $0.041667 \times \$300 \text{ million} = \$12.50 \text{ million}$.