The monthly demand equation for an electric utility company is estimated to be p=61105x, where p is measured in dollars and x is measured in thousands ofkillowatt-hours. The utility has fixed costs of $5,000,000 per month and variable costs of $33 per 1000kilowatt-hours of electricitygenerated, so the cost function is C(x)=5106+33x.

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

(b) Suppose that the rising fuel costs increase theutility's variable costs from $33 to $41, so its new cost function is C1(x)=5106+41x. Should the utility pass all this increase of $8 per thousandkilowatt-hours on to theconsumers?