Final answer:
The minimum number of investors needed to vote for a change in top management at the Darkroom Windowshade Company is at least 6 investors. If investors 1 and 2 vote together, they can always have their way in how the company is run.
Step-by-step explanation:
The minimum number of investors it would take to vote to change the company's top management is determined by the total number of shares needed for a majority vote. In this case, the company has 100,000 shares outstanding.
To calculate the number of shares needed for a majority vote, we add up the number of shares held by the investors: 20,000 + 18,000 + 15,000 + 10,000 + 7,000 + (5,000 * 6) = 97,000 shares.
Since a majority vote requires more than 50% of the shares, the minimum number of investors needed for a majority vote is at least 6 investors.
However, if investors 1 and 2 agree to vote together, they can control a total of 38,000 shares, which is more than 50% of the total shares outstanding. Therefore, if investors 1 and 2 vote together, they can be certain of always getting their way in how the company will be run.