Final answer:
A minimum of three investors is necessary to change the company's top management. Investors 1 and 2, with a combined 38,000 shares, cannot always secure decisions without additional shareholder support.
Step-by-step explanation:
To address the schoolwork question, we first need to evaluate the individual shareholdings of the investors in the Darkroom Windowshade Company. Considering the company has 100,000 shares of stock outstanding, a simple majority (> 50%) is required to enact significant changes like altering top management. Thus, more than 50,000 shares must be voted in a particular way to ensure control over such decisions.
Now, assessing the share distribution among investors: investor 1 has 20,000 shares, investor 2 has 18,000 shares, investor 3 has 15,000 shares, investor 4 has 10,000 shares, investor 5 has 7,000 shares, and investors 6 through 11 have 5,000 shares each. Collectively, investors 1 and 2 hold 38,000 shares. To surpass the 50% threshold, their combined shares need to be at least 50,001. Hence, they would require support from additional investors.
To find the minimum number of investors needed to change the company's top management, one can start by combining the largest shareholders until surpassing the 50,000 mark. Investor 1 (20,000) and Investor 2 (18,000) can form a block with 38,000 shares. Adding investor 3 (15,000) reaches 53,000 shares, crossing the majority threshold. Therefore, it would take a minimum of three investors to change the company's top management.
If investors 1 and 2 agree to vote together, their block of 38,000 shares is not sufficient on its own to guarantee outcomes as they are still short of the 50,001 votes needed for a majority decision. They can influence, but not always secure, decisions without support from additional shareholders.