Question

an investor has $215,000 to distribute between two investments. let x be the portion invested in the first option. how much should the investor put into the first investment option to minimize risk if the risk function is r(x) = 0.055x² - 0.096x + 0.048? round your answer to the nearest thousand. enter your answer in the box. $

Explanation:

Step1: Identify quadratic vertex formula

For $R(x)=ax^2+bx+c$, vertex at $x=-\frac{b}{2a}$

Step2: Plug in coefficients

$a=0.055$, $b=-0.096$
$x=-\frac{-0.096}{2\times0.055}=\frac{0.096}{0.11}\approx0.8727$

Step3: Calculate dollar amount

Total funds: $\$215000$
Amount $=215000\times0.8727\approx187630.5$

Step4: Round to nearest thousand

$\approx188000$

Answer:

$\$188000$