Suppose that the cost function in Exercise 45 is C(x) = -2.5x + 1, where x% is the index-fund fee. (The company has a fixed cost of $1 billion, and the cost decreases as a function of the index-fund fee.) Find the value of x that maximizes profit. How well did Fidelity Mutual do before and after lowering the index-fund fees?

Exercise 45

When a mutual fund company charges a fee of 0.47% on its index funds, its assets in the fund are $41 billion. And when it charges a fee of 0.18%, its assets in the fund are $300 billion.