Final answer:
To change the management of the Darkroom Windowshade Company, more than 50% of the shares need to vote in favor. With investors 1 and 2 voting together, they still fall short of the majority. They need support from at least one more investor, and with investor 3, they would control a voting majority.
Step-by-step explanation:
The student's question pertains to the number of investors needed to change the management of a company given the number of shares each investor holds. To change the top management, a simple majority of more than 50% is necessary. The Darkroom Windowshade Company has 100,000 shares outstanding. If investors 1 and 2 vote together, they control a total of 20,000 + 18,000 = 38,000 shares. As the company has 100,000 shares out, a simple majority would be anything over 50,000 shares. Therefore, investors 1 and 2 alone could not guarantee always getting their way as they control less than 50%.
To achieve a majority, they would need support from at least investor 3, who has 15,000 shares, bringing the total to 53,000 shares. Thus, the minimum number of investors needed to change the company's top management would be three, assuming investors 1, 2, and 3 vote together.