Question

a tour operator charge rs 200 per passenger for 50 passenger with a discount of rs 5 for each 10 passenger in excess of 50 determine the number of passengers that will maximize the revenue of the operator​

Answer 1

Given :   a tour operator charge rs 200 per passenger for 50 passenger with a discount of rs 5 for each 10 passenger in excess of 50

To find : determine the number of passengers that will maximize the revenue of the operator​

Solution:

operator charge rs 200 per passenger for 50 passenger

Revenue = 200 * 50  = Rs 10000

discount of rs 5 for each  10 passenger in excess of 50

Let say 10P  Passenger in excess of 50  then  

Charges 200  - 5P

Revenue = (200 - 5P)(50 + 10P)

=> R = 10000 + 2000P - 250P  - 50P²

=> R = 10000 + 1750P - 50P²

dR/dP =  1750  - 100P

=> 1750 - 100P = 0

=> P = 17.5

d²R/dP² =    - 100   < 0

Hence Maximum revenue at   P = 17.5

but P has to be integer  so lets Check at

P = 17    & P = 18

Revenue = (200 - 5P)(50 + 10P)

P = 17 => R =  (200 - 85) (50 + 170)  =  25300

P = 18 => R =  (200 - 90) (50 + 180)  =  25300

Passengers  = 220  or 230    will maximize the revenue of the operator​

if We consider 17.5 also

Then  R =   (200 - 87.5) (50 + 175)  =  25312.5

Passengers = 225

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