HW1a_Solutions

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Oregon State University, Corvallis *

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392

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Civil Engineering

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Apr 3, 2024

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docx

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Homework 1- Solutions January 4, 2021 CE 392 Introduction to Highway Engineering Chapter 1 Garber and Hoel These 3 problems are open-ended Problems 1-11 1-14 1-15 Chapter 2 Garber and Hoel Problems 2-1 2-3 2-4 2-5 2-7 2-13 2-16

Homework 1- Solutions January 4, 2021 2-1 ( 5 points ) How would your typical day be changed without availability of your principal mode of transportation? Consider both personal transportation as well as goods and services that you rely on. Example answer: A typical day in my life would be significantly different without the airplane. Although I do not use this mode daily, goods and services that I do purchase are transported via this mode. Other modes, such as trucking, trains, and the automobile, could serve as replacements to the airplane; however, the airplane significantly lowers the transit time for shipping goods. For example, I mail a letter to California. Typical transit time for this letter using the airplane is three days. By using another mode other than the airplane, the transit time for the same letter would probably exceed seven days. As for my personal transportation, long distance travel is accomplished by using the airplane. For example, I take a vacation to Europe. If I travel using a cruise ship, it would take me in excess of seven days to reach Europe. However, if I fly, I can arrive in Europe within nine hours. Having the ability to transport people and goods quickly allows the international trade market to prosper, which in turn provides me with goods in a timely and efficient manner.

Homework 1- Solutions January 4, 2021 2-3 ( 20 points ) A bridge has been constructed between the mainland and an island. The total cost (excluding tolls) to travel across the bridge is expressed as C = 50 + 0.5V, where V is the number of veh/hr and C is the cost/vehicle in cents. The demand for travel across the bridge is V = 2500 −10C . (a) Determine the volume of traffic across the bridge. (b) If a toll of 25 cents is added, what is the volume across the bridge? (c) A tollbooth is to be added, thus reducing the travel time to cross the bridge. The new cost function is C = 50 + 0.2V. Determine the volume of traffic that would cross the bridge. (d) Determine the toll to yield the highest revenue for demand and supply function in part (a), and the associated demand and revenue. (a) Determine the volume of traffic across the bridge. Substitute the total cost function into the demand function and solve for V. V = 2500 –10(50 + 0.5V) V = 2500 – 500 – 5V 6V = 2000 V = 333.33 vehicles/ hour Therefore, the number of vehicles wanting to cross this bridge is 334 vehicles/hour. (b) If a 25 cent toll was added, what is the new volume crossing the bridge? 1. Add 25 cents to the original cost function. C = 50 + 0.5V + 25 C = 75 + 0.5V Substitute the above cost function into the demand function and solve for V. V = 2500 – 10(75 + 0.5V) V = 2500 – 750 – 5V 6V = 1750 V = 291.667 Therefore, the new volume crossing the bridge will now be 292 vehicles / hour with a 25 cents toll.

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