Final answer:
The minimum number of investors needed to vote for a change in top management is determined by the total number of outstanding shares. Investors 1 and 2 cannot be certain of always getting their way in how the company will be run.
Step-by-step explanation:
The minimum number of investors it would take to vote to change the company's top management is determined by the total number of outstanding shares required to reach a majority. In this case, the company has 100,000 shares of stock outstanding. To reach a majority, more than 50,000 shares need to be voted in favor of the change. The investors with the highest number of shares are investors 1 and 2, who together own 38,000 shares. Therefore, with the support of these two investors, at least three additional investors with a total of at least 12,000 shares need to vote in favor of the change in order to reach a majority.
However, even with the support of investors 1 and 2, they cannot be certain of always getting their way in how the company will be run. This is because there are other investors who collectively own a significant number of shares (investors 3 to 11 own a total of 55,000 shares). If these investors vote together, they could still influence the decision-making process and potentially prevent investors 1 and 2 from always getting their way.