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. (Source: The Boston Globe.)

(a) Let x % denote the fee that the company charges the index fund and A(x) its assets in the fund. Express A(x) as a linear function of x.

(b) In September 2004, Fidelity Mutual lowered its fees on various index funds from an average of 0.3% to 0.10%. Let R(x) denote the revenue of the company from fees when its index-fund fee is x%. Compare the revenue of the company before and after lowering the fees.

(c) Find the fee that maximizes the revenue of the company and determine the maximum revenue.