Final answer:
To change the company's top management, shareholders with a combined majority of over 50% of shares need to agree. In the case of the Darkroom Windowshade Company, Investors 1 and 2 would need to join forces with at least Investor 3 to achieve this majority. Without majority support, Investors 1 and 2 cannot always be certain of getting their way.
Step-by-step explanation:
Calculating Shareholder Control in Companies
To determine the minimum number of investors required to vote to change the company's top management in the Darkroom Windowshade Company, one must calculate the percentage of shares each investor holds and then find the smallest combination of investors whose combined share ownership exceeds 50% of the total shares. A simple majority (over 50%) is typically required to make significant decisions such as changing the company's top management.
In this case, the company has 100,000 shares outstanding. Investor 1 and Investor 2 together hold 20,000 shares and 18,000 shares, respectively. Combining their shares, they own 38,000 shares out of 100,000, which accounts for 38% of the total voting power. This is not enough to ensure control since they would need more than 50%. Therefore, they would need support from additional investors to reach a majority vote. If they were to gain the support of Investor 3, who owns 15,000 shares, their combined total would be 53,000 shares, exceeding 50% and allowing them to control decisions.
However, if any combination of the other shareholders (Investor 3 to 11) decided to vote together and their combined votes total over 50%, then Investors 1 and 2 would not be able to control the company's decisions, even when voting together. It is important to note that majority control is situational and depends on the distribution of the remaining shares.