A portfolio manager wants to distribute $60,000 between two investments. The risk function is R(x)=0.029x^2−0.018x+0.009 . If x is the portion invested in the first option, how should the manager distribute the funds to minimize risk? Round your answer to the nearest thousandth if necessary.
Answer
A
First option: 0 point 1 9 Second option: 0 point 8 1
B
First option: 0 point 3 1 0 Second option: 0 point 6 9
C
First option: 0 point 8 1 Second option: 0 point 1 9
D
First option: 0 point 6 9 Second option: 0 point 3 1 0
Explanation
The risk function is a quadratic that opens upward because the coefficient of x² is positive (0.029), so its minimum occurs at the vertex. Set its derivative, 0.058x − 0.018, equal to zero to get x = 0.018 ÷ 0.058 ≈ 0.310; the remaining portion is 1 − 0.310 = 0.690. The manager should invest 0.310 in the first option and 0.690 in the second, which is choice B.
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