Final answer:
To change the Darkroom Windowshade Company's top management, a group needs a majority of shares. Investors 1 and 2, with 38,000 shares combined, would need to partner with at least Investor 3 to surpass the 50% threshold. With Investor 3, this coalition can control the company's decisions.
Step-by-step explanation:
To determine the minimum number of investors needed to change the company's top management at Darkroom Windowshade Company, one must gather a majority which is over 50% of the voting power, given there are 100,000 shares outstanding. This means that any voting group needs to hold more than 50,000 shares to have a majority. As investor 1 has 20,000 shares and investor 2 has 18,000 shares, combined they have 38,000 shares. This alone is not enough to ensure they always get their way in how the company is run. They would need to align with at least one more investor, such as investor 3 who has 15,000 shares, to surpass the 50,000 threshold and have a controlling interest. Therefore, the minimum number of investors needed to change the company's top management would be three: investors 1, 2, and 3. If investors 1 and 2 vote together with investor 3, they can be certain of controlling the company's decisions with a total of 53,000 shares.