If X Dollars Is Invested in a Company That Controls $0.3 x$

Multiple Choice

If x dollars is invested in a company that controls, say, 30 percent of the market with 5 brand-names, then $0.3 x$ is a measure of market exposure and $5 x$ is a measure of brand-name exposure. Now suppose you are a broker at a large securities firm, and one of your clients would like to invest up to $100,000 in recording industry stocks. You decide to recommend a combination of stocks in four of the world's largest companies: Warner Music, Universal Music, Sony, and EMI. $$\begin{array} { | c | c | c | c | c | } \hline & \text { Warner Music } & \text { Universal Music } & \text { Sony } & \text { EMI } \\\hline \text { Market Share } & 12 \% & 20 \% & 20 \% & 15 \% \\\hline \begin{array} { c } \text { Number of } \\\text { brand-names }\end{array} & 8 & 20 & 10 & 15 \\\hline\end{array}$$
You wanted your client to maximize his total market exposure but limit his brand-name exposure to 2 million or less (representing an average of 20 labels or fewer per company) , and still invest at least 20 percent of the total in Universal. How much should you advise your client to invest in each company

A) $20,000 in Warner Music, $80,000 in Sony, and no investment in Universal Music and EMI
B) $80,000 in Warner Music, $20,000 in EMI, and no investment in Universal Music and Sony
C) $20,000 in Universal Music, $80,000 in Sony, and no investment in Warner Music and EMI
D) $80,000 in Warner Music, $20,000 in Sony, and no investment in Universal Music and EMI
E) $80,000 in Universal Music, $20,000 in Sony, and no investment in Warner Music and EMI