The monthly demand equation for an electric utility company is estimated to be p = 64 - (10 ) x, where p is measured in dollars and x is measured in thousands of killowatt-hours. The utility has fixed costs of $3,000,000 per month and variable costs of $38 per 1000 kilowatt-hours of electricity generated, so the cost function is C(x) = 3 . 10 + 38x. (a) Find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. (b) Suppose that the rising fuel costs increase the utility's variable costs from $38 to $52, so its new cost function is C, (x) = 3 . 10 + 52x. Should the utility pass all this increase of $14 per thousand kilowatt-hours on to the consumers? (a) Find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. x = (Type an integer or a decimal.)