A local club is arranging a charter flight to Hawaii The cos

A local club is arranging a charter flight to Hawaii. The cost of the trip is $554 each for 83 passengers, with a refund of $5 per passenger for each passenger in excess of 83. Find the number of passengers that will maximize the revenue received from the flight. Find the maximum revenue. The number of passengers that will maximize the revenue received from the flight is . (Round to the nearest integer as needed.) The maximum revenue is $ .

Solution

qa let # of passengers be (83 + x) revenue R = $ (554 - 5x)(83+x) = 45982 + 554x - 5*83x - 5x^2 = 45982 + 139x - 5x^2 dR/dx = 139-10x & d2R/dx2 is -ve, so to maximize revenue, dR/dx = 0,which gives x = 13.9 =>14 # of passengers for max revenue = 83 + 14 = 97 qb max revenue = (554 - 5*14)(97) = $46,948 ans: ----- (a) 97 (b) $46,948