Final answer:
To change top management, shareholders with over 50% of the stock must agree. Investors 1 and 2, with 38,000 shares combined, would need Investor 3 to surpass the majority with 53,000 shares. Without such a coalition, Investors 1 and 2 cannot ensure control.
Step-by-step explanation:
The student's question revolves around understanding the ownership and control dynamics of a corporation by analyzing the distribution of stock among its shareholders. To determine the minimum number of investors required to change the company's top management, one would need to ascertain the majority vote threshold, which is more than 50% of the outstanding shares, in this case over 50,000 shares. As the Darkroom Windowshade Company has 100,000 shares outstanding, Investor 1 and Investor 2, holding 20,000 and 18,000 shares respectively, would have a combined shareholding of 38,000 shares.
To exert full control and always have their way in managing the company, Investors 1 and 2 would need to align with at least one more investor. Considering that Investor 3 holds 15,000 shares, their collective would then control 53,000 shares, which would be enough to pass the majority vote. Without such a coalition, Investor 1 and Investor 2 could not be certain of always getting their way in company decisions.