Final answer:
To change the top management of The Darkroom Windowshade Company, a majority of over 50,001 shares is needed. A minimum of three investors is required, with Investors 1 and 2 needing additional support since they only control 38,000 shares together. Investors 1 and 2 cannot guarantee getting their way without the support of other shareholders.
Step-by-step explanation:
To change the company's top management, a majority vote is required. This usually means over 50% of the voting power. With 100,000 shares outstanding, a majority would be at least 50,001 shares. The minimum number of investors needed to reach this majority can be determined by cumulatively adding the number of shares held by investors from the largest shareholder to the smallest, until the majority is surpassed.
Investor 1 holds 20,000 shares; Investor 2 holds 18,000 shares; together, they collectively hold 38,000 shares. Adding Investor 3's 15,000 shares brings the total to 53,000 shares, which is a majority. Therefore, it takes a minimum of three investors to change the company's top management.
When Investors 1 and 2 vote together, they hold 38,000 shares, which is not a majority. They need the support of at least one more investor with any number of shares to surpass the 50% threshold. Hence, they cannot be certain of always getting their way in how the company is run unless they form a coalition with other investors.