Q1

The manufacturer of GRIPPER tires modeled its return to sales from television advertising expenditures in two regions, as follows: Region 1: S, = 20 + 34x1 - 0.8x1 2 Region 2: S, = 40 + 24X2 - 1.3x2 2 where S, and S, are the sales revenue in millions of dollars and x, and x2 are millions of dollars of expenditures for television advertising. (Round your answers to three decimal places.) (a) What advertising expenditures would maximize sales revenue in each district? Region 1 $ million Region 2 $ million (b) How much money will be needed to maximize sales revenue in both districts? $ millionThe profit per acre from a grove of orange trees is given by x(170 - x) dollars, where x is the number of orange trees per acre. How many trees per acre will maximize the profit? trees per acreAnalysis of daily output of a factory during a 8-hour shift shows that the hourly number of units y produced after t hours of production is 2 y = 70t + +2 - +3, osts8. (a) After how many hours will the hourly number of units be maximized? hr (b) What is the maximum hourly output? units/hrTwo equal rectangular lots are enclosed by fencing the perimeter of a rectangular lot and then putting a fence across its middle. If each lot is to contain 1,200 square feet, what is the minimum amount of fence (in ft) needed to enclose the lots (include the fence across the middle)? Step 1 Study the diagram below to confirm that it accurately depicts the given problem. X X y 1200 y y X X If fencing is to enclose the rectangles and go through the middle, the diagram shows that there are 4 sections of fencing x feet long and sections of fencing y feet long. amount of fencing needed is the sum of these sections. Write an equation for the total amount of fence needed F in terms of x and y. F = 4x + We are given that the area of each rectangle in the diagram above is 1,200 square feet. Write an equation for area A in terms of x and y. A = X . Then, substitute the given value for A. =X . y Next, solve for y. 1,200Find any horizontal and vertical asymptotes for the function. (Enter your answers as a comma-separated list of equations. If an answer does not exist, enter DNE.) 9x y = x - 8 horizontal asymptotes vertical asymptotesTutorial Exercise A function and its first and second derivatives are given. Use these to find any horizontal and vertical asymptotes, critical points, relative maxima, relative minima, and points of inflection. Then sketch the graph of the function. X y = (x - 2) 2 x+ 2 y' = = (x - 2)3 2x + 8 y" = (x - 2)4 Step 1 Begin by finding the asymptotes. First determine any horizontal asymptotes. (If an answer does not exist, enter DNE.) X lim x -+ 0 (x - 2)2 So, there is a horizontal asymptote at The vertical asymptote is any value of x that makes the denominator (but not the numerator) zero. Thus, for y = X (x - 2)2, the only vertical asymptote is at the following