Calculus, please help with both parts a & b. Thank you

The monthly demand equation for an electric utility company is estimated to be p = 85 - (10 _ 5) x, where p is measured in dollars and x is measured in thousands of killowatt-hours. Theutility has fixed costs of $3,000,000 per month and variable costs of $47 per 1000 kilowatt-hours of electricity generated, so the cost function is C(x) = 3 - 106 + 47x. (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 $47 to $59, so its new cost function is C1(x)= 3 -106 + 59x. Should the utility pass all this increase of $12 perthousand 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=|Z| (Type an integer or a decimal.)