Final answer:
Change the Darkroom Windowshade Company's top management, the minimum number of shareholders needed is three—investors 1, 2, and 3—because together they hold a majority of 53,000 shares. Investors 1 and 2 alone do not have a majority and thus cannot be certain of getting their way without additional support.
Step-by-step explanation:
The method used when an investor has control through voting interests, and ownership is more than 50%, is known as having a controlling interest. In the scenario of the Darkroom Windowshade Company with 100,000 shares outstanding, to change the company's top management, more than 50% of the voting power is required, which is at least 50,001 shares. To achieve this, the minimum number of investors needed would depend on how many shares each investor controls.
Since the question gives the share distribution, we can calculate that investor 1 with 20,000 shares and investor 2 with 18,000 shares have a combined total of 38,000 shares. Together, they do not have a majority. The next largest shareholder, investor 3, holds 15,000 shares. If investors 1, 2, and 3 agree to vote together, they would have a combined total of 53,000 shares, giving them a majority vote capable of effecting change in management. Thus, the minimum number of investors needed to vote to change the company's top management is three.
If investors 1 and 2 agree to vote together, they still need additional shares to always ensure they can get their way. They cannot be certain of always getting their way in how the company is run without holding a majority of shares themselves or through agreement with other shareholders.