Final answer:
A minimum of three investors is needed to change the company's top management as 53,000 shares are required for a majority. Investors 1 and 2, with 38,000 shares when voting together, do not have a majority and thus cannot be certain of controlling the company.
Step-by-step explanation:
To determine the minimum number of investors required to vote to change the company's top management, we need to calculate the majority shareholding. Since there are 100,000 shares outstanding, a majority would require more than 50,000 shares to agree.
Starting from the largest shareholder, we add up the shares until we surpass 50,000. Investor 1 has 20,000 shares, and investor 2 has 18,000 shares, which together account for 38,000 shares. Adding investor 3's 15,000 shares brings the total to 53,000 shares, which is enough to form a majority. Therefore, the minimum number of investors needed is three.
If investors 1 and 2 agree to vote together, they control 38,000 shares, which is not a majority. Without a majority, they cannot be certain of always getting their way in how the company is run. They would need at least one more investor to join them to ensure control over the company decisions.