Question

A book designer has decided that the pages of a book should have 1-in. margins at the top and bottom and 1/2-in. margins on the sides. She further stipulated that each page should have an area of 32 in.2 (see the figure below). Determine the page dimensions that will result in the maximum printed area on the page. 1 in. Need Help? Read It Watch It 18. -14 points v TANAPMATH7 10.5.019. My Notes | Ask Your Teacher v If exactly 206 people sign up for a charter flight, Leisure World Travel Agency charges $300/person. However, if more than 206 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Hint: Let x denote the number of passengers above 206. Find the revenue function R(x). R(x) = Determine how many passengers will result in a maximum revenue for the travel agency. passengers What is the maximum revenue? What would be the fare per passenger in this case? dollars per passenger

Answer 1

1 xy=32 y = 32 Area of pointed portion = (x - 12 - 2)(y-1-1) A = (x-1)(y-2) = xy - 2x - 4+2 = A= 32 - 2x - 32+2 for maximum printed area A = 0 d (32- 2x - 32 - 2 + 2) = 0 > 0-2 -32x2 to 20 – 2 + 32 = 0 - 32 = 2 x ² = 16 = x=4 Thus dimension of page x=Gin, y=32 = 18 in 18 x is additional passenger, fare = $300-x) gevenue R(x) = (206+x)(300-2). R(x) = 61800 +942-x²] for maximum revenue al(R(u) =0 = a (61800 +942 - x² = 0 =) 0+94-2x = 0 = xe = 47 total passenger = 206+47 = 12537 maximum Revenue = 61800 +94447-472 - $64009 fare per passenger =$300-47) = [$253 ax