A portfolio manager wants to distribute $200,000 between two investments. The risk function is R(x)=0.073x^2−0.092x+0.046 If x is the portion invested in the first option, how should the manager distribute the funds to minimize the risk? Round the answer to the nearest whole number if necessary.
Answer
A
First option: 120 dollars comma 000 Second option: 80 dollars comma 000
B
First option: 74 dollars comma 000 Second option: 126 dollars comma 000
C
First option: 126 dollars comma 000 Second option: 74 dollars comma 000
D
First option: 80 dollars comma 000 Second option: 120 dollars comma 000
Explanation
Since the coefficient of x² is positive, the risk is minimized at the quadratic’s vertex. The vertex occurs at x = −(−0.092)/(2 × 0.073) ≈ 0.6301, so about 63.01% of the $200,000 should go into the first option: approximately $126,000. The remaining $74,000 goes into the second option, matching choice C.
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