Question

A transit company carries about 80 000 riders per day for a fare of $1.25. To obtain more revenue, the management plans to increase the fare. It estimates that for every 5 cent increase in fare, it will lose 1000 riders. What fare would result in the greatest revenue and what would the maximum revenue be?

Answer 1

To find the fare that would result in the greatest revenue, we need to consider the relationship between the fare and the number of riders. Increasing the fare results in a decrease in the number of riders. The fare that results in the greatest revenue is $2.20 and the maximum revenue is $100,000.

Step-by-step explanation:

To find the fare that would result in the greatest revenue, we need to consider the relationship between the fare and the number of riders. We know that increasing the fare by 5 cents will result in a loss of 1000 riders. This means that for every 5 cent increase, the number of riders will decrease by 1000.

To maximize revenue, we need to find the fare that generates the maximum product of the fare and the number of riders. Let's analyze the relationship between the fare and the number of riders:

1. Current fare: $1.25, Number of riders: 80,000
2. Fare increase by 5 cents: $1.30, Number of riders: 79,000
3. Fare increase by 10 cents: $1.35, Number of riders: 78,000
4. Fare increase by 15 cents: $1.40, Number of riders: 77,000

From this analysis, we can see that as the fare increases, the number of riders decreases. Therefore, we should stop increasing the fare when the number of riders reaches zero. This occurs when the fare is $2.20 ($1.25 + 19 * $0.05).

The maximum revenue can be calculated by multiplying the fare by the number of riders at that fare. At a fare of $2.20, the number of riders will be zero, and the revenue will also be zero. Therefore, the maximum revenue that can be generated is $1.25 * 80,000 = $100,000.

Answer 2

It would probably be 2 - 3 cents they could add