Daniel_Lougee_Wk2 Assignment
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Defense Language Institute *
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500
Subject
Mathematics
Date
Feb 20, 2024
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Running head: ASSIGNMENT WEEK 2 (MATH)
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ASSIGNMENT WEEK 2 (MATH)
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Assignment Week 2 (Math)
Question A
Trip Adjustment Factor:
In trip calculation, it is observed that a Wal-Mart store driver successfully made a total of 120 trips in a given period of time. During field calculation, it is shown that the calculated number of trips is actually 144. What is the value of the adjustment factor? To determine the trip adjustment from 120 trips to 144 trips one must use the standard formula for adjustment factor. Sinha & Labi identify the formula for trip adjustment factor as adjustment factor or Kij = Tji observed activity over Tji actual calculated trips (2007.) The number of observed trips and actual calculated trips are given and formulate in this manner: Kij = Tji(observed) / Tji(actual) Kij = 120 (observed) / 144 (actual)
Kij (Trip Adjustment Factor) = 0.8333
Question B
Travel Demand:
It is shown that the population of New York City, NY is much greater than that of Irvington, NJ. Employment opportunities, malls, social activities and tourist sites in New York City are therefore more than that in Irvington. If attractiveness for New
York and Irvington are therefore 1,600 and 160 respectively and if the calculated impedance of migration is known to be 1.57, based on Gravity-Based model, estimate in
ASSIGNMENT WEEK 2 (MATH)
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demands, the number of people who travel between Irvington, NJ and New York City per
week.
In order to identify the estimated travel demand between Irvington NJ and NYC per any given week one must apply travel demand formula. Travel demand formula is demonstrated by Sinha & Labi, (2007) through which VAB (demand for transportation between two locations) = NA (City A Attractiveness) * NB (City B Attractiveness) * IAB
(Travel Impedance for both locations) or VAB=NA*NB*IAB. The attractiveness of both city A and city B are given and reflect as NA=1600, NB=160. The travel impedance is also given and reflects as IAB 1.57. All variables calculate on a basis of one week unit. The travel demand formula calculates as such:
NA = 1600 / week
NB = 160 / week
IAB = 1.57 / week
VAB = 1600 * 160 * 1.57 / week
VAB (Estimated Travel Demand) = 401,920/week
Question C
Linear Aggregate Demand:
Elasticity can be defined as percentage change in demand for a 1% change in decision attribute. For linear aggregate demand, what is the mathematical representation/formula for this statement? You must define the parameters you choose to use for this answer. The mathematical representation of linear aggregate demand defined by Sinha & Labi, (2007) is percent change in demand e
x
(V) = x
∂
V
(variable) / V
∂x (elasticity). In this statement the percentage of change in demand is 1% but there are no definitive
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variables. Therefore, the mathematical representation reads as e
x
(V) = x
∂
V
*
0.01. Variable X is open to any possible trip demand adjusting factor such as trip vector. Question D
Arc Elasticity of Vehicle Traffic: In the City of Joplin, due to weather devastation and hurricane effects, the cost of parking in the local Square has increased by 15%. This change has not only reduced the number of vehicles that travel to the Square by 10%, but it has also forced the inhabitants of Joplin to use buses. Bus trips have therefore increased
to 25%. With respect to the cost of parking in the local Square, determine the elasticity of
vehicle traffic. Arc of Elasticity of Vehicle traffic formula is required to determine the elasticity of vehicle traffic in the city of Joplin. Sinha & Labi, (2007) define Arc of Elasticity of Vehicle formula as ETP = V (P1 initial parking price + P2 final parking price) / 2 over p(V1 initial transit demand + V2 final transit demand) / 2 = (VA2 final auto demand - VA1 initial auto demand) * (P1 initial parking price + P2 final parking price) / 2 over (P2
final parking price – P1 initial parking price) * (VA1 initial auto demand +VA 2 final auto demand) / 2 = -0.25. The unknown factors are initial parking price or P1, initial transit demand or V1, and initial auto demand or VA1. Final parking price is equal to the previous price with a 15% increase and reflects as P2 = 1.15 * P1. The final transit demand has increased 25% and reflects as V2 = 1.25 * V1. The final demand on vehicles decreased 10% reflecting as
VA2 = 0.90 * VA1. The Arc of Elasticity of Vehicle traffic formula calculates as such:
P1 = P1
P2 = 1.15 * P1
ASSIGNMENT WEEK 2 (MATH)
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V1 = V1
V2 = 1.25 * V1
VA1 = VA1
VA2 = 0.90 * VA1
ETP = (VA2 - VA1) * (P1 + P2) / 2 / (P2 - P1) * (VA1 + VA2) / 2
= (0.90 * VA1 - VAL) (P1 + 1.15 * P1) / 2 / ((1.15 * P1 – P1) * (VA1 + 0.90 * VA1) / 2)
0.25 * 1.90 = 0.475 / 2 = 0.2375
-0.10 * 2.15 = -0.215 / 2.00 = -0.1075 / 0.2375 = -0.4526
Elasticity of vehicle traffic = -.4525
Question E
Average Cost:
In your own words, describe the meaning of average cost. You normally buy a crate of wine for $75. One crate has 8 bottles of wine. After a month, the store clerk
informs you that the same crate of wine now costs $82. However, there are 10 bottles in a
crate. To the nearest cent, determine the average cost of the crate from last month to now.
Average cost is the cost of an individual quantity as extrapolated from its division of the whole. To obtain the average cost of a crate over a given duration of time one can use the standard formula for solving average cost. As defined by Sinha & Labi (2007), the formula is Average Total Cost (ATC) = Total Cost / Volume, Average Fixed Cost = Fixed Cost / Volume, or Average Variable Cost = Variable Cost / Volume. In this problem the known variables are previous cost and volume and new cost and volume. Change in average cost comes from comparing the two total cost averages from past month to current as seen below:
Previous month average cost = $75.00 / 8 bottles = $9.38 per bottle
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Current month average cost = $82.00 / 10 bottles = $8.20 per bottle
$75.00 / case – $82.00 / case = $7.00 a case higher $9.38 - $8.20 = $1.18 per bottle less than the previous month.
The total cost of a case increased $7.00 from the previous month but the individual cost per bottle decreased $1.18 from the previous month.
Question F
Marginal Cost:
In your own words, describe the meaning of marginal cost. You normally buy a crate of wine for $75. One crate has 8 bottles of wine. After a month, the store clerk informs you that the same crate of wine now costs $82. However, there are 10 bottles in a crate. To the nearest cent, determine the marginal cost for one additional bottle of wine now.
Marginal cost is a representation of the cost to increase production by a quantity of one. Sinha & Labi find marginal cost by dividing change in cost over change in volume (2007.) In the sample problem the original and new costs as well as volume are known. The marginal cost of one additional bottle of wine comes from the cost of an individual bottle prior compared against the variance of a new bottle.
$75 / 8 bottles = 9.38
$82 / 10 bottles = 8.20
$9.38 - $8.20 = $1.18
The marginal cost for one additional bottle of wine is now $1.18 less.
Question G
Unit Travel: In your own words, describe the meaning of unit travel. When traveling on a Greyhound bus, without intervention or obstruction, it is important to determine the unit
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travel time. If you leave Cleveland in a bus full of 30 passengers and arrive in Cincinnati in 4 hours, what will be the average unit travel time in person minutes?
Unit travel is the average time duration that an individual traveler remains in a conveyance for a trip duration. According to Sinha & Labi (2007), the formula for Unit Travel is U1 = OCC (average occupancy) * TTv (average vehicle operating time). Given the known factors, OCC = 30 passengers and a travel time of TTV = 4 hours or 4 * 60 = 240 minutes, the formula is as follows:
U1=OCC * TTv
U1= 30 passengers * 240 minutes = 7200 average unit travel time in person minutes
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References
Sinha, K. C., & Labi, S. (2007). Transportation decision making: Principles of project evaluation and programming
. Hoboken, NJ: John Wiley & Sons, Inc.