The monthly demand equation for an electric utility company is estimated to be p = 60 - (10^-5)x, where p is measured in dollars and x is measured in thousands of kilowatt-hours. The utility has fixed costs of 7 million dollars per month and variable costs of $30 per 1000 kilowatt-hours of electricity generated, so the cost function is C(x) = 7 · 106 + 30x.

(a) Find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility’s profit.

(b) Suppose that rising fuel costs increase the utility’s variable costs from $30 to $40, so its new cost function is C1(x) = 7 · 106 + 40x.

Should the utility pass all this increase of $10 per thousand kilowatt-hours on to consumers? Explain your answer.