A person has \(\$ 4000\) available initially for investment in two risky ventures A and B. Venture A will return nothing in a time period with probability \(2 / 3\), and will return \(\$ 3000\) per thousand invested with probability \(1 / 3\). Venture B will return either \(\$ 1000\) or \(\$ 2000\) per thousand invested, each with probability \(1 / 2\). Investment amounts are in units of a thousand dollars, and the person may risk as much as \(\$ 2000\) per time period. Find the strategy that maximizes the expected value of the square of the terminal wealth at the end of 2 time periods.