(a)
The expression for travel demand on the bridge related to toll increase and current volume.
Answer to Problem 4P
The expression for travel demand on the bridge related to toll increase and current volume is
Explanation of Solution
Given:
A toll bridge carries
The current toll is
For each increase in toll of
Concept used:
Write the relation between traffic volume and cost.
Here,
Calculations:
Substitute
Conclusion:
Therefore, the expression for travel demand on the bridge related to toll increase and current volume is
(b)
The toll charge to maximize revenue.
Answer to Problem 4P
The toll charge to maximize the revenue is
Explanation of Solution
Write the expression to calculate the total toll charge.
Here,
Write the expression to calculate the revenue generated.
Here,
Calculations:
Calculate the total toll charge.
Substitute
Calculate volume of traffic expected for a 50 cent increase.
Substitute
For maximum value, calculate the first derivative of above equation and equate to zero.
Substitute
Conclusion:
Therefore, the toll charge to maximize revenue is
(c)
The traffic volume after toll increase.
Answer to Problem 4P
The traffic volume after toll increase is
Explanation of Solution
Calculations:
Calculate the traffic volume after toll increase.
Consider the expression for travel demand on the bridge related to toll increase and current volume.
Substitute
Conclusion:
Therefore, the traffic volume after toll increase is
(d)
The total revenue increase with new toll.
Answer to Problem 4P
The total revenue increase with new toll is
Explanation of Solution
Calculations:
Substitute
Conclusion:
Therefore, the total revenue increase with new toll is
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Chapter 2 Solutions
Traffic And Highway Engineering
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