Answer to Question #304523 in Calculus for Anniee

Question #304523

A commuter train carries 600 passengers each day from a town to a city. A one-way trip costs 100 per person. Market research reveals that 10 fewer people would ride the train with every 1 increase in the fare. What fare should be charged to get the largest possible revenue?

1
Expert's answer
2022-03-02T16:54:25-0500

Here the variables are

x,x, the number of passengers,

p,p, the price per ticket,

and R,R, the revenue.

We have

R=pxR = px


We obtain


R=p(60010(p100)).R = p(600 -10(p-100)) .

R=10p2+1600p,p100R=-10p^2+1600p, p\ge100

a=10<0,pv=b2a=16002(10)=80a=-10<0, p_v=-\dfrac{b}{2a}=-\dfrac{1600}{2(-10)}=80

R(80)=10(80)2+1600(80)=64000R(80)=-10(80)^2+1600(80)=64000

The revenue has the absolute maximum with value of 64000 at price 80.



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