The demand function for the luminar desk lamp is given by p = f(x) = −0.1x2 − 0.3x + 20 where x is the quantity demanded in thousands and p is the unit price in dollars. (a) find f '(x). f '(x) = −.2x−.3 (b) what is the rate of change of the unit price when the quantity demanded is 7000 units (x = 7)? $ per 1000 lamps what is the unit price at that level of demand

Suppose life expectancy in years (l) is a function of two inputs, health expenditures (h) and nutrition expenditures (n) in hundreds of dollars per year. the production function is upper l equals ch superscript 0.40 baseline upper n superscript 0.60l=ch0.40n0.60. beginning with c = 1, a health input of $400400 per year (hequals=44) and a nutrition input of $400400 per year (nequals=44), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing. the marginal product of health expenditures when h goes from 44 to 55 is nothing, and the marginal product of health when h goes from 66 to 77 is nothing. (round your answers to three decimal places.)

Your sister turned 35 today, and she is planning to save $60,000 per year for retirement, with the first deposit to be made one year from today. she will invest in a mutual fund that's expected to provide a return of 7.5% per year. she plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. under these assumptions, how much can she spend each year after she retires? her first withdrawal will be made at the end of her first retirement year.

The year is 2278, and the starship enterprise is running low on dilithium crystals, which are used to regulate the matter-antimatter reactions that propel the ship across the universe. without the crystals, space-time travel is not possible. if there is only one known source of dilithium crystals, the necessary conditions for a monopoly are met. part 2 (1 point)see hint if the crystals are government owned or government regulated, and the government wants to create the greatest welfare for society, then it should set the price choose one or more: a. so only the rich can afford space-time travel. b. at the profit-maximizing price. c. at the efficient price. d. using the marginal-cost pricing rule. e. so everyone can afford space-time travel. f. at the monopoly price.