Final answer:
A minimum of three investors (Investors 1, 2, and 3) is required to change The Darkroom Windowshade Company's top management, as they would have a combined total of 53,000 shares, surpassing the 50% mark. Investors 1 and 2 alone do not hold a majority and cannot ensure control without additional support.
Step-by-step explanation:
The question asks about the minimum number of investors required to change the top management of The Darkroom Windowshade Company, which has 100,000 shares outstanding. To change management, an investor group needs more than 50% of the voting power, meaning they need to own more than 50,000 shares. Investor 1 and investor 2 together own 38,000 shares. Therefore, even if they vote together, they would not be capable of changing the company's top management on their own.
Let's calculate the smallest coalition that could achieve a majority. Adding Investor 3's shares (15,000) to Investor 1 and 2's shares makes a total of 53,000 shares. Therefore, the minimum number of investors needed to change the company's top management would be three (Investors 1, 2, and 3).
If Investor 1 and Investor 2 try to get their way in how the company is run by voting together, they would have a combined total of 38,000 shares, which is not a majority. Therefore, they cannot be certain of always getting their way unless they form a larger coalition with other investors.