If X Dollars Is Invested in a Company That Controls

Short Answer

If x dollars is invested in a company that controls, say, 30 percent of the market with 5 brand-names, then 0.3x 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 3.5 million or less (representing an average of 35 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
$__________ in Warner Music, $__________ in Universal Music, $__________ in Sony, and $__________ in EMI.