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

I don't know how to do it either but the answer in the textbook says $2.00

I did this already today.

Charge 50 cents

To determine the price that will maximize revenue, we need to understand the relationship between the price, the number of riders, and the revenue.

Let's start by analyzing how the number of riders changes as the ticket price increases. We know that for every 10 cents increase, the number of riders decreases by 400. So, if the price increases by $1, we would have 10 groups of 10 cents, which means the number of riders will decrease by 10 * 400 = 4000.

Now, let's calculate the number of riders at different price points:

- At $1 per ticket, the number of riders is 12000.
- At $1.10 per ticket, the number of riders will be 12000 - 4000 = 8000.
- At $1.20 per ticket, the number of riders will be 12000 - 2 * 4000 = 4000.
- At $1.30 per ticket, the number of riders will be 12000 - 3 * 4000 = 0.

Next, let's calculate the revenue at each price point. The revenue is equal to the price per ticket multiplied by the number of riders.

- At $1 per ticket, the revenue is 1 * 12000 = $12000.
- At $1.10 per ticket, the revenue is 1.10 * 8000 = $8800.
- At $1.20 per ticket, the revenue is 1.20 * 4000 = $4800.
- At $1.30 per ticket, the revenue is 1.30 * 0 = $0.

The maximum revenue occurs when the price per ticket generates the highest revenue, which is $12000. From the calculations, we can see that this price is $1.

Therefore, the price for a ticket that will maximize revenue is $1.