Let c(q) represent the cost and r(q) represent the revenue, in dollars, of producing q items. (a) if c(50)=4300 and c′(50)=21, estimate c(54) . c(54)=$ (b) if c′(50)=21 and r′(50)=36, approximately how much profit is earned by the 51st item? the profit on the 51st item is dollars. (c) if c′(100)=40 and r′(100)=36, should the company produce the 101st item? the company produce the 101st item. click if you would like to show work for th

Amathematical approximation called the rule of 70 tells us that the number of years that it will take something that is growing to double in size is approximately equal to the number 70 divided by its percentage rate of growth. thus, if mexico's real gdp per person is growing at 7 percent per year, it will take about 10 years(=70/7) to double. apply the rule of 70 to solve the following problem. real gdp per person in mexico in 2005 was about $11,000 per person, while it was about $44,000 per person in the u.s. if real gdp per person in mexico grows at the rate of 5 percent per year: how long will it take mexico's real gdp per person to reach the level that the united states was at in 2005? (hint: how many times would mexico's 2005 real gdp per person have to double to reach the u.s.'s 2005 real gdp per person?

Last year, johnson mills had annual revenue of $37,800, cost of goods sold of $23,200, and administrative expenses of $6,300. the firm paid $700 in dividends and had a tax rate of 35 percent. the firm added $2,810 to retained earnings. the firm had no long-term debt. what was the depreciation expense?

David paid $975,000 for two beachfront lots in coastal south carolina, with the intention of building residential homes on each. two years later, the south carolina legislature passed the beachfront management act, barring any further development of the coast, including david's lots. when david files a complaint to seek compensation for his property, south carolina refuses, pointing to a passage in david's own complaint that states "the beachfront management act [was] properly and validly designed to south carolina's " is south carolina required to compensate david under the takings clause?