Final answer:
A minimum of three investors is needed to change the company's top management, with Investors 1, 2, and 3 controlling a combined total of over 50% of the shares. Investors 1 and 2 together do not hold a majority and cannot ensure always getting their way without additional support.
Step-by-step explanation:
To determine the minimum number of investors required to vote to change the company's top management, we need to consider the overall distribution of shares. For a change to occur, more than 50% of the voting power, which corresponds to the number of shares, would need to be in favor. 51,000 shares, representing just over 50% of the total shares, would constitute this majority.
Investor 1 has 20,000 shares, and Investor 2 has 18,000 shares. Combined, they have 38,000 shares. The minimum number of additional investors needed to reach the 51,000 threshold would be Investor 3 with 15,000 shares, giving them a cumulative total of 53,000 shares. Therefore, it would take at least three investors (Investors 1, 2, and 3) to achieve a majority.
Even if Investors 1 and 2 vote together, they do not control a majority of the shares on their own. Their combined voting power is 38,000 shares, which is less than the 51,000 needed for a majority. Therefore, they cannot be certain of always getting their way in how the company is run without the support of additional investors.