Asked by Debo
a City's transit authority serves 178500 communters daily when the fare is $1.90. Market research has determined that every penny decrease in the fare will result in 1,050 new riders. what fare will maximize revenue?
Answers
Answered by
Steve
revenue = #riders * fare
= (178500+1050(190-x))(.01x) for x<=190
that's just a parabola with vertex at x=180.
= (178500+1050(190-x))(.01x) for x<=190
that's just a parabola with vertex at x=180.
Answered by
Reiny
number of penny decreases ---- n
cost of fare = 190-n
number of riders = 178500 + 1050n
revenue = R = (190-n)(178500+1050n)
P' = (190-n)(1050) + (178500 + 1050n)(-1)
= 0 for a max of P
178500 + 1050n = 1050(190-n)
divide by 1050
170 + n = 190-n
2n = 20
n = 10
the fare should be 190+10 = 200
or it should be $ 2.00
cost of fare = 190-n
number of riders = 178500 + 1050n
revenue = R = (190-n)(178500+1050n)
P' = (190-n)(1050) + (178500 + 1050n)(-1)
= 0 for a max of P
178500 + 1050n = 1050(190-n)
divide by 1050
170 + n = 190-n
2n = 20
n = 10
the fare should be 190+10 = 200
or it should be $ 2.00
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.