Final answer:
Investor 1 and 2 together do not hold a majority; they need additional investors to pass a vote. The minimum number would include them and several smaller shareholders to exceed 50,000 shares. They cannot be certain of always getting their way without the support of others.
Step-by-step explanation:
To determine the minimum number of investors required to vote to change the company's top management, we must establish what constitutes a majority vote. A majority in this case would require more than half of the 100,000 shares to be in agreement. The investors' ownership of shares is as follows: Investor 1 owns 20,000 shares; Investor 2 owns 18,000 shares; Investor 3 owns 15,000 shares; Investor 4 owns 10,000 shares; Investor 5 owns 7,000 shares; and Investors 6 through 11 own 5,000 shares each.
Adding up the shares owned by the largest shareholders, we find that Investor 1 and Investor 2 together hold 38,000 shares. This is not a majority. Therefore, to achieve a majority, they would need support from either Investor 3 or a combination of several smaller shareholders (Investors 4, 5, 6, 7, 8, 9, 10, 11). The minimum number of investors needed for a majority, without Investor 3, would sum up to Investor 1, 2, 4, 5, and at least three of the remaining investors to surpass the 50,000 mark. With Investors 1 and 2 combining their shares, they hold 38% of the company and therefore cannot be certain of always getting their way in decisions about how the company is run without the support of other shareholders.