Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with retirement income of $20,000 per month for 25 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $380,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $900,000 to his nephew Frodo. He can afford to save $2,500 per month for the next 10 years. The APR before retirement is 9.57% and the APR after retirement is 6.78%. How much will he have to save each month in years 11 through 30

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?