Final answer:
The minimum number of investors required to vote to change the company's top management is 3. Investors 1 and 2 cannot be certain of always getting their way in how the company will be run.
Step-by-step explanation:
The Darkroom Windowshade Company has 100,000 shares of stock outstanding. To determine the minimum number of investors it would take to vote to change the company's top management, we need to calculate the total number of shares held by investors other than investors 1 and 2.
Investor 1 holds 20,000 shares and investor 2 holds 18,000 shares, so the combined total of their shares is 38,000. The remaining investors hold 15,000 + 10,000 + 7,000 + (5,000 * 6) = 63,000 shares. To achieve a majority vote, we need to find the smallest number of investors who together hold more than 50,000 shares. Since the remaining investors hold a total of 63,000 shares, it would take a minimum of 3 additional investors to vote together to change the company's top management.
Investors 1 and 2 can be certain of always getting their way in how the company will be run if they have more than 50% of the total shares. To determine if they have more than 50%, we calculate the total number of shares held by all investors, which is 20,000 + 18,000 + 15,000 + 10,000 + 7,000 + (5,000 * 6) = 100,000 shares. The shares held by investors 1 and 2 represent 20,000 + 18,000 = 38,000 shares. Since 38,000 is less than 50% of 100,000, investors 1 and 2 cannot be certain of always getting their way in how the company will be run.