Question

all instructions carefully. Answer questions neatly on a separate sheet of paper. 1.(15 pts) Total revenue (in billions) for Exxon-Mobile Corp. can be approximated for n 2000 hroh 201S by R)21.5x + 516x -2614, where x-0 coresponds to the earaurs or the s to the year a. Use the derivative to determine the timeframes the revenue was increasing and decreasing. b. What year did a local maximum in revenue occur, and what was the revenue that 2. (15 points) A group of researchers found that people prefer training videos of moderat g video Shorter films contain too little information, while longer films are boring. For a trainin for the care of exotic birds, the researchers determined that the ratings gave for the film could be 20t by the function R(2,900 whee t is the length of the film in minutes. approximated t2 +100 a. Use the derivative to determine the length of film that got the best rating. b. What was the rating? 3. (20 points) One store's revenue from selling designer handbags is approximated by the function R(x) = (200x)e-01x a) How many handbags should be sold to maximize revenue? b) What is the maximum revenue? c) When revenue is at a maximum, what is the average price per bag? 4. (25 Points) A mathematics book is to contain 36 square inches of printed material per page. Page margins are 1 inch along the sides and 1.5 inches along the top and bottom. Find the dimensions of the page that will lead to the minimum amount of paper being used. 1.5in in36in lin 1.5in

Answer 1

@ X2+ 5.6% 2.614 RG. = - 21-S - 43 12 RGaximom atx12 2. 2 46 200 200