The city bus company usually transports 12000 riders per day at a ticket price of $1. The company wants to raise the tickets price and knows that for every 10 cents increase, the number of riders decreases by 400.

Question

The city bus company usually transports 12000 riders per day at a ticket price of $1. The company wants to raise the tickets price and knows that for every 10 cents increase, the number of riders decreases by 400.
A. What price for a ticket will maximize revenue?
pls help

Anono · Accepted Answer

Little late, but the answer is two dollars according to the textbook

Damon · Answer

n riders, q price increase over 100 pennies in pennies

n = 12000 (1 - 400 *10q)

r = n ( 100 + q)

so

r = 12000 (1-4000q)(100+q)

r = 12000 (100 -399,999 q - 4,000q^2)

dr/dq = 12000 (-399,999 - 8,000 q)
max when 0
q = about -50 cents
looks like they should lower the price to 50 cents to maximize revenue

If you do not do calculus find the vertex of the parabola
40 q^2 + 4000q -1 = 0