Question

The city transit system carries 24,800 bus riders per day for a fare of $1.85. The city hopes to reduce car pollution by getting more people to ride the bus while maximizing the transit system's revenue at the same time. A survey indicates that the number of riders will increase by 800 for every $0.05 decrease in the fare. What fare will produce the greatest revenue?

a) $1.85
b) $1.80
c) $1.75
d) $1.70

Answer 1

To find the fare that will produce the greatest revenue, we need to determine the relationship between the number of riders and the fare. Evaluating the revenue for each fare option, we find that the fare that will produce the greatest revenue is $1.70.

Step-by-step explanation:

To find the fare that will produce the greatest revenue, we need to determine the relationship between the number of riders and the fare. From the survey, we know that the number of riders will increase by 800 for every $0.05 decrease in fare. This means that the demand curve for bus riders is a linear equation with a slope of -800 and a y-intercept of 24,800.

We can use the demand curve to calculate the revenue for each fare option. The revenue is given by the product of the number of riders and the fare. Evaluating the revenue for each fare option, we find that:

• For a fare of $1.85, the revenue is $1.85 * 24,800 = $45,880
• For a fare of $1.80, the revenue is $1.80 * (24,800 + 800) = $46,320
• For a fare of $1.75, the revenue is $1.75 * (24,800 + 2 * 800) = $46,680
• For a fare of $1.70, the revenue is $1.70 * (24,800 + 3 * 800) = $46,960

Therefore, the fare that will produce the greatest revenue is $1.70.