Final answer:
A minimum of 3 investors with a combined total of 53,000 shares can vote to change the Darkroom Windowshade Company's top management. Investors 1 and 2, with 38,000 shares, cannot be certain of always getting their way as they do not hold a majority on their own.
Step-by-step explanation:
In the context of the Darkroom Windowshade Company, which has 100,000 shares of stock outstanding, to change the company's top management, a majority vote is required. This means more than 50,000 of the shares would need to be voted in favor of the change, as this would constitute more than 50% of the available votes. To calculate the minimum number of investors needed, one would have to tally up the largest shareholdings until this majority is reached. Starting with the largest shareholder, you have 20,000 shares from investor 1, adding 18,000 shares from investor 2 gives a total of 38,000 shares. Adding investor 3 with 15,000 shares increases the total to 53,000 shares, which is a majority. Therefore, a minimum of 3 investors can change the top management.
If investors 1 and 2 agree to vote together, they would hold a combined total of 38,000 shares. While this is a significant portion, it is not enough to ensure they can always get their way in how the company is run, since it does not represent a majority. They would still require the support of at least one additional investor to reach a majority vote.