Final answer:
To change The Darkroom Windowshade Company's top management, a minimum of three investors is needed to surpass the majority threshold of 50,000 votes. Investors 1 and 2 combined have 38,000 shares; thus, they need additional support to have a majority.
Step-by-step explanation:
The question asks what the minimum number of investors would be required to vote to change the company's top management for The Darkroom Windowshade Company, which has 100,000 shares of stock outstanding. To achieve a majority, more than 50% of the vote is necessary, which equates to more than 50,000 votes. Investors 1 and 2 combined have 38,000 shares, so they cannot be certain of always getting their way in how the company is run without additional support since 50,000 is required for a majority.
To determine the minimum number of investors needed to achieve the majority, we add up the shares from the largest to the smallest holdings until we surpass the 50,000 threshold. Here is how the shares add up: Investor 1's 20,000 shares + Investor 2's 18,000 shares + Investor 3's 15,000 shares reach a total of 53,000 shares, achieving a majority. Therefore, the minimum number of investors needed would be three.