Final answer:
A minimum of three investors are needed to change the company's top management when combining the shares of investor 1, 2, and 3. Investors 1 and 2, even when voting together, cannot always get their way, as they control 38% of shares and need over 50% to assure their influence.
Step-by-step explanation:
The minimum number of investors required to vote to change the top management depends on how many shares collectively represent more than 50% of the total shares, as a majority is usually required to make such a decision. In the case of the Darkroom Windowshade Company, a combination of investors 1 and 2, who have 20,000 and 18,000 shares respectively, would control 38,000 shares out of 100,000, which is not a majority. They would need at least one more shareholder to join them to have the power to change the management. Adding investor 3's 15,000 shares gives them a total of 53,000, which is just over 50%, making the minimum number of investors needed to change management three (investors 1, 2, and 3).
If investors 1 and 2 agree to vote together, they would control 38% of the company. However, they cannot be certain of always getting their way in how the company will be run since they do not have a majority on their own. They would need to form alliances with other shareholders to ensure they have over 50% of the voting power.