Jim and Kay Ross contributed to the support of their two children, Dale and Kim, and Jim's widowed parent, Grant. During the year, Dale, a 19-year-old full-time college student, earned $5,500 as a babysitter. Kim, a 23-year-old bank teller, earned $12,000. Grant received $5,000 in dividend income and $4,000 in nontaxable Social Security benefits (dividends, but not social security benefits, will be included in Grant's gross income). Kim and Grant currently reside with Jim and Kay. Dale's main place of residence is with Jim and Kay, and he is currently on a temporary absence to attend school. How many dependents can Jim and Kay claim on their joint income tax return?

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?