The monthly demand equation for an electric utility company is estimated to be p equals 60 minus left parenthesis 10 superscript negative 5 baseline right parenthesis x​, where p is measured in dollars and x is measured in thousands of​ killowatt-hours. the utility has fixed costs of ​$3 comma 000 comma 000 per month and variable costs of ​$32 per 1000​ kilowatt-hours of electricity​ generated, so the cost function is upper c left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 32 x. ​(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 ​$32 to ​$38​, so its new cost function is upper c 1 left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 38 x. should the utility pass all this increase of ​$6 per thousand​ kilowatt-hours on to the​ consumers?