Final answer:
To change the company's top management, the minimum number of investors required is three, combining investors 1, 2, and 3's shares to surpass the majority threshold. Investors 1 and 2 together do not hold a majority and thus cannot dictate company management decisions without additional support.
Step-by-step explanation:
To determine the minimum number of investors needed to vote to change the top management at Darkroom Windowshade Company, one must first ascertain the majority shareholder threshold. With 100,000 shares outstanding, more than 50,000 shares must vote in favour to achieve a majority. Secondly, if investors 1 and 2 combine forces, they possess a total of 38,000 shares (20,000 + 18,000). Though substantial, this does not constitute a majority on its own.
To establish the minimum number of investors required, let's start with investor 1, who has 20,000 shares, and add other investors with the most shares until the majority is reached. Adding investor 2's 18,000 shares and investor 3's 15,000 shares, the sum is 53,000 shares, which is enough to pass the majority threshold. Therefore, at least three investors are needed to change the company's top management.
However, investors 1 and 2 alone lack the majority with their combined 38,000 shares. Therefore, they cannot be assured of always getting their way in how the company is run unless they secure additional support from other shareholders.