An average of 6000 passengers a day takes the city subway trains at the cost of $3 per ride. The city board is thinking about raising the price to $3.50 per ride in order to generate larger revenue. They talk to a consulting team whose study shows that for each $0.50 increase in price, the number of passengers would be reduced by an average of 1000 a day. The consulting team suggests the city board should leave the price of $3 per ride since it already yields the maximum revenue. Prove that the consulting team is correct.