Final answer:
A minimum of three investors is required to change Darkroom Windowshade Company's top management, as 53,000 shares would constitute a majority. Investors 1 and 2, with a combined 38,000 shares, cannot always get their way without additional support.
Step-by-step explanation:
To find out the minimum number of investors required to change the company's top management, one must ascertain what constitutes a majority share. In a company with 100,000 shares outstanding, a majority would be more than half, hence at least 50,001 shares are needed for a majority vote. Starting with the largest shareholder, we can add up the shares until this number is surpassed. Investor 1's 20,000 shares and Investor 2's 18,000 shares total 38,000 shares. Adding Investor 3 with 15,000 gives us 53,000 shares, which is a majority. Therefore, it would take a minimum of three investors to achieve a majority vote and change the company's top management.
If investors 1 and 2 agree to vote together, they would control 38,000 shares. To be certain of making decisions regarding the company's management, they would need to surpass the 50,000-share threshold. As they do not meet this requirement on their own, they cannot be certain of always getting their way in how the company is run without the support of additional investors.