Traffic and Highway Engineering
Traffic and Highway Engineering
5th Edition
ISBN: 9781305156241
Author: Garber, Nicholas J.
Publisher: Cengage Learning
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Chapter 2, Problem 3P
To determine

(a)

The volume of traffic across the bridge.

Expert Solution
Check Mark

Answer to Problem 3P

The volume of traffic across the bridge is 333.33veh/hr.

Explanation of Solution

Given:

The total cost to travel across bridge except tolls is expressed as,

  C=50+0.5V.

Here, V is the number of vehicles per hour and C is the cost/veh in cents.

The demand to travel across the bridge is,

  V=250010C.

Calculations:

Calculate volume of traffic across the bridge.

The total cost to travel across bridge except tolls is,

  C=50+0.5V ....... (I)

The volume across the bridge is,

  V=250010C ....... (II)

Solve Equations (I) and (II).

  C=216.67

  V=333.33

Conclusion:

Therefore, the volume of traffic across the bridge is 333.33veh/hr.

To determine

(b)

The volume of traffic across the bridge if a toll of 25cents is added and for 50cents increase.

Expert Solution
Check Mark

Answer to Problem 3P

The volume of traffic across the bridge if a toll of 25cents is added is 291.67veh/hr and for 50cents increase is 327.49veh/hr.

Explanation of Solution

Concept used:

Write the expression to calculate the volume expected for a 50cents increase.

  V=V(V new50)

Here, Vnew is the volume of traffic across the bridge if toll is increased to 25cents and V is the volume of traffic across the bridge.

Calculations:

Calculate volume of traffic across the bridge if toll is increased to 25cents.

The new cost of the cost of travel across bridge is,

  C=50+0.5V+25

Substitute (50+0.5V+25) for C in Equation (II).

  V=2,50010(50+0.5V+25)V=2,5005005V2506V=1,750V=291.67

Calculate volume of traffic expected for a 50cents increase.

Substitute 333.33veh/hr for Vnew and 291.67veh/hr for V in Equation (II).

  V=333.33veh/hr( 291.67 veh/ hr 50)=333.33veh/hr5.8334veh/hr=327.49veh/hr

Conclusion:

Therefore, the volume of traffic across the bridge if a toll of 25cents is added is 291.67veh/hr and for 50cents increase is 327.49veh/hr.

To determine

(c)

The volume of traffic across the bridge.

Expert Solution
Check Mark

Answer to Problem 3P

The volume of traffic across the bridge is 666.67veh/hr.

Explanation of Solution

Given:

The total cost to travel across bridge including toll is expressed as,

  C=50+0.2V

Calculations:

Calculate volume of traffic across the bridge.

Substitute (50+0.2V) for C in equation (II).

  V=2,50010(50+0.2V)V=2,5005002V3V=2,000V=666.67

Conclusion:

Therefore, the volume of traffic across the bridge is 666.67veh/hr.

To determine

(d)

The toll to yield the highest revenue for demand and supply function and the associated demand and revenue.

Expert Solution
Check Mark

Answer to Problem 3P

The toll which yield the highest revenue for demand and supply function is $1.00, associated demand is 166.67veh/hr and revenue. $16,666,67 per hour.

Explanation of Solution

Concept used:

Write the expression to calculate the revenue generated.

  R=V×T ....... (III)

Here, R is the revenue and T is the toll.

Calculations:

Assume the toll rate as T to yield highest revenue.

The new cost of the cost of travel across bridge is,

  C=50+0.5V+T

Substitute (50+0.5V+T) for C in Equation (II).

  V=2,50010(50+0.5V+T)V=2,5005005V10T6V=2,00010TV=2,00010T6 ....... (IV)

Substitute (2,00010T6) for V in Equation (III).

  R=( 2,00010T6)×T=2,000T10T26 ....... (V)

From the above equation, the toll which would yield the maximum revenue is 100 cents or $1.00.

Substitute 100 for T in Equation (V).

  R=2,000( 100)10 ( 100 )26=2,00,0001,00,0006=1,00,0006=16,666,67

Calculate the demand for travel across the bridge for maximum revenue.

Substitute 100 for T in equation (IV).

  V=2,00010( 100)6=2,0001,0006=1,0006=166.67

Conclusion:

Therefore, the toll which yield the highest revenue for demand and supply function is $1.00, associated demand is 166.67veh/hr and revenue. $16,666,67 per hour.

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