When a mutual fund company charges a fee of 0 42% on its index funds, its assets in the fund are $37 billion When ll charges a fee of 0 19% its assets in the fund are $211 billion (a) Let x denote the fee that the company charges as a percentage ofthe index fund and lelA(x) denote its assets in the fund Express A(x) as a linear function of x. (b) One company lowers its fees on various index funds from an average of 033% to 0 11% Let R(x) denote the revenue ofthe company from fees when its indexefund fee is x" Compare the revenue of the company before and alter lowering the fees [Hint Revenue is x% of the assets ] (c) Find the fee that maximizes the revenue of the company and determine the maximum revenue (a) Let x denote the fee that the company Charges as a percenmge ofthe index fund and letA(x) denote its assets in the fund Express A00 as a linear function of x NX) : (Simplify your answer Use integers or decimals for any numbers in the expression Round to three decimal places as needed) (b) One company lowers its fees on various index funds from an average of 0 33% to 0 1 1% Let R(x) denote the revenue of the company from fees when its indexefund fee is X'Vn Compare the revenue of the company before and after lowering the fees, [Hint Revenue is x% of the assets] Rm : (Use integers or decimals for any numbers in the expression Round to three decimal places as needed) When the fees were lowered from 033% to 0 11%' the revenue of the company V by 515 billion (Type an integer or a decimal Round to three decimal places as needed ) (c) Find the fee that maximizes the revenue ofthe company and determine the maximum revenue The fee that maximizes the revenue of the company is % (Type an integer or a decimal Round to three decimal places as needed.) The maximum revenue of the company IS 5; billion (Type an integer or a decimal Round to three decimal places as needed )