Question

A local club is arranging a charter flight to Hawaii. The cost of the trip is $595 each for 82 passengers, with a refund of $5 per passenger for each passenger in excess of 82. Write a function for the revenue from the flight as a function of the number of passengers over 82.. Revenue can be found by multiplying the number of passengers by the cost each passenger must pay. Let x represent the number of passengers over 82. R(x)- 2. a. b. Find the marginal revenue for the flight c. What number of passengers will maximize revenue? d. What is the revenue when the number of passengers is 82? R e. Wha passengers t is the maximum revenue? R

Answer 1

a. Revenue(x) = (82+x)*(595-5x) = 48790-410n+595n-5n^2 = 48790+185n-5n^2
b. MR =185-10n
c. Revenue(x) = 48790+185n-5n^2
Solving for n, we get n=18.5 or 19 and TR = 50501.25 and hence total passenger = 101
d. Revenue = Q*P = N*595 = 82*595 = 48790
e. Maximum revenue = $50501.25

For c. by substituting x=0 to 20 we can verify that revenue gets maximized at x=19

x	Revenue
0	48790
1	48970
2	49140
3	49300
4	49450
5	49590
6	49720
7	49840
8	49950
9	50050
10	50140
11	50220
12	50290
13	50350
14	50400
15	50440
16	50470
17	50490
18	50500
19	50500
20	50490
21	50470