Final answer:
A minimum of three investors (investors 1, 2, and 3) with a combined 53,000 shares could vote to change the company's top management, as this constitutes a majority. Investors 1 and 2 combined own 38,000 shares, which is not enough to ensure they always get their way without additional support.
Step-by-step explanation:
To determine the minimum number of investors needed to vote for a change in top management at the Darkroom Windowshade Company, we must first understand that a majority of the 100,000 shares outstanding must approve the change. A majority would be over 50,000 shares. When we add the shares owned by the investors in descending order, we find that investors 1, 2, and 3 hold a total of 53,000 shares (20,000 + 18,000 + 15,000), which is enough to secure a majority.
As for whether investors 1 and 2 can always get their way in how the company is run if they vote together, we must consider their combined share total. Together, they hold 38,000 shares (20,000 + 18,000). This is not a majority, as it falls short of the over 50,000 shares needed. As a result, investors 1 and 2 cannot be certain of always getting their way. They would require the support of at least one more investor to surpass the 50,000 threshold for a majority vote.