10/24/2013
ME6105 G3
Value-Driven Problem Definition
Group Members:
ZACKARY PITTS – JOEL GRINDSTAFF – JOSEPH HICKEY – THOMAS CAHUZAC
Table of Contents
I.
Task 1: Become Familiar with ModelCenter: ..................................................................................................... 2
II.
Task 2: Revisit the Decision Situation identified in HW G1:............................................................................... 2
A.
Influence Diagram .......................................................................................................................................... 2
B.
Application Domain: ...................................................................................................................................... 3
C.
System Description: ....................................................................................................................................... 3
D.
Assumptions:.................................................................................................................................................. 4
E.
Important Performance Attributes: ............................................................................................................... 4
F.
Decision Maker: Who are we as the decision maker? ................................................................................... 5
III.
Task 3: Cost Modeling: ................................................................................................................................... 6
A.
Motor Pricing and Simulation Specification Calculations: ............................................................................. 6
1.
DC Motor Model Calculations: ................................................................................................................... 6
i.
Manufacturer Specification and Motor Specification used in Dymola Model:..................................... 6
ii.
Price Approximation: ............................................................................................................................... 7
B.
Lithium Battery and Simulation Specific Calculations: .................................................................................. 8
C.
Weight and Simulation Specific Calculations: .............................................................................................. 10
IV.
Task 4: Identify and Model the Remaining Relationships:........................................................................... 10
A.
Introduction: ................................................................................................................................................ 10
B.
Obtained Graph: .......................................................................................................................................... 11
C.
Interpretation: ............................................................................................................................................. 14
V.
Task 5: Integrate and validate your models:.................................................................................................... 15
VI.
Task 6: Interpretation: ................................................................................................................................. 22
A.
Where did you struggle? .............................................................................................................................. 22
B.
Where did you go down the wrong path? ................................................................................................... 22
C.
Did you learn anything new about the trade-offs in the system you were designing? ............................... 22
VII.
Task 7: Update Project Web-page ............................................................................................................... 23
VIII.
Index Table of Figures: ................................................................................................................................. 24
1|Page
I.
Task 1: Become Familiar with ModelCenter:
The process of wrapping the Dymola models was basically taken straight from the video lectures. First all the
software had to be downloaded and installed. Then, by dragging the Quick Wrap tool into the work area, a prompt
appeared and the files for input, output and the executable files had to be specified. The input file tab prompted for an
input file to be selected which was chosen to be the dsin file located where the Dymola model had been run. Then
through a fairly tedious process, the variables of interest to be modified during the test runs had to be identified,
selected, and named. The use of bookmarks allowed for a more reliable way for Model Center to find the variables
and an easier way for the user to navigate around the text file. Once all the inputs were specified, the same process
was followed for the outputs. These variables will come out of the dsfinal file and go into other models in Model
Center. Then the executable file had to be specified. The dynoism.exp file is used by model Center to run the
simulation each time it needed to produce updated values for each run. After this a test was run by selecting the green
triangle icon in the top right corner of the window. The test produced a template file and returned a notice that the
run was successful. This procedure was followed for two Dymola models. At this point the quick wrap was done.
The process for wrapping the Excel files was much more straight forward. The Excel plugin icon was dragged into the
work area and the variables were identified with new names and the corresponding cells for input and output were
selected.
II.
Task 2: Revisit the Decision Situation identified in HW G1:
A.
Influence Diagram
After talking to the TA, it became evident that our influence diagram for this assignment should only include the
parameters that we will be simulating. As a result we took the influence diagram from the previous assignment and
updated it accordingly.
The updated influence diagram from Homework G1 appears in the figure below:
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Figure 1. Influence diagram for electric bike
B.
Application Domain:
In this project, we will be designing a bicycle with an integrated electric motor. The bicycle will be electrically
powered and will be legally confined to very specific engineering parameters. These legal requirements include:
-
C.
Maximum power output of electrical motor is 250 Watts
Electric motor will only help the rider if speed of bike remains under 15 mph. As a result, electric motor
will shut down when bike speed exceeds 15 mph
System Description:
The bike will be powered by the biker through pedaling and by the electric motor. As a result if the speed of the bike is
under 15 mph the bike will be electrically and “manually” (pedaling) powered. Once again please note that when the
bike speed exceeds 15 mph, the bike will only be manually powered and the electric motor will shut off.
Please note that a means network diagram will be presented a bit further down in the report for your convenience.
Here is an extremely simplified version of the bike that shows how we broadly modeled the bike. Please understand
that this is not intended to be a detailed representation of our electric bike.
3|Page
Figure 2. Top Level Broad Design
D.
Assumptions:
The following assumptions will be made:
-
E.
No physical deformation of bike frame
No slip between wheels and road surface
The bike will be considered to be travelling in one dimension with hills and other resistances being
represented as a force along the axis of motion
The bike frame will be modeled as a simple mass
Important Performance Attributes:
The important performance attributes of our system will be as follows:
Climbing ability: We will measure the hill climbing ability of an electric assisted bicycle without user
input.
Range: Our goal will be to optimize the overall range of the bike.
Minimize the weight of the system: We will be trying to minimize the overall weight of the system.
For your convenience, we have introduced the means objective network below:
-
4|Page
Figure 3. Means Network for Electronic Bike
F.
Decision Maker: Who are we as the decision maker?
We work for a company in the design and research group. Our ultimate goal is to maximize profit for the company. We
have been told by management that this can be done by optimizing range, minimizing costs and designing a bike that
can complete a pre-selected course in as little time as possible. The fact that it can complete the course in such a short
time will be used in the marketing campaign of the new product.
Our role as the decision maker will be as follows:
Consider different ideas and solution variants
Translate client needs and desires into engineering specification
Come up with engineering solutions to solve problems
Our abilities as the decision maker must be as follows:
Must be able to work as a group, bringing in talent from different engineering fields
Ability to extract key issues
Negotiate between client and design team
Ability to assess complex processes
Ability to plan complex processes
Ability to continuously monitor actual and target parameters
It is our belief that the decision scenario is scoped within our authority. Our goal is to provide the best suited product
in accordance with clients’ needs and desires. Optimizing range, speed and minimizing friction losses lie at the core of
what clients want when purchasing an electric bike.
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III.
Task 3: Cost Modeling:
A.
Motor Pricing and Simulation Specification Calculations:
1.
DC Motor Model Calculations:
Motor equations are as follows:
𝑉 = 𝑖𝑅 + 𝐿
𝜏 = 𝑏𝜔 + 𝐽
𝑑𝑖
𝑑𝑡
𝑑𝜔
𝑑𝑡
+ 𝐾ω
(1)
+ 𝐾𝑖
(2)
Consider steady state equation:
𝑑𝑖
𝑑𝑡
= 0;
𝑑ω
𝑑𝑡
(3)
=0
Using equation (1), (2) and (3), one can obtain the following equations below. Please note that these are the values
which we will be inputting into our Dymola model.
𝐾=
11𝑉𝑛𝑜𝑚
𝑅 = 1.1
𝑏=
(4)
10𝜔𝑚𝑎𝑥
𝑉𝑛𝑜𝑚2
(5)
𝜏𝑠𝑡𝑎𝑙𝑙 𝜔𝑚𝑎𝑥
𝜏𝑠𝑡𝑎𝑙𝑙
(6)
40𝜔𝑚𝑎𝑥
i. Manufacturer Specification and Motor Specification used in Dymola Model:
The motors for our electric bike will be obtained from the McMaster Carr Website. After talking to them on the phone
we were able to understand that a 15% discount would be applied to any order for over 1000 units. As a result we
have adjusted the prices below. Here are the manufacturer specification supplied by the manufacturer as well as the
appropriate motor specifications that were calculated.
Table 1. Manufacturer and Motor Specification
Manufacturer Specification
hp
ω (rpm)
Torque (in-lbs)
Serial Number
Price ($)
Vnom (V)
0.10
4200
1.8
59835K61
142.99
24
0.14
4200
2.56
59835K62
165.27
24
0.25
3500
6.38
59835K63
221.36
24
0.33
3900
5.88
59835K64
233.28
24
Motor Specification
K
b
Pmax (W)
0.006286
Torque (N.m)
0.203373
R (Ω)
0.741775668
4.28571E-05
213.54165
0.006286
0.2892416
0.521561016
6.09524E-05
303.70368
0.007543
0.7208443
0.251134082
0.000182286
630.7387625
0.006769
0.6643518
0.244541429
0.000150769
647.743005
The weights of the various motors are provided below, please note that because the information was not available
online, we elected to call the manufacturer directly to acquire the information:
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Table 2. Motor Weights
Motor Weight
Serial Number
Weights (lbs)
Weight (kg)
59835K61
5.25
2.381359943
59835K62
6
2.72155422
59835K63
9
4.08233133
59835K64
10
4.5359237
ii. Price Approximation:
Let us start by graphing Power (W) vs. Price ($):
Power (W) vs Price ($)
700
y = 5.1035x - 524.47
R² = 0.9913
600
Power (W)
500
400
300
200
100
0
0
50
100
150
200
250
Price ($)
Figure 4 Price ($) vs. Power (B) of Motor for sampled Motors
As a result we have managed to come up with a simple equation relating Power (W) and Price ($) for the motor that
we will be using.
(7)
𝑃𝑜𝑤𝑒𝑟 (𝑊) = 5.1035 ∗ 𝑃𝑟𝑖𝑐𝑒($) − 524.47
For convenience let us flip the equation to obtain an easy way to calculate price with power as an input.
𝑃𝑟𝑖𝑐𝑒 ($) =
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20[52447+100∗𝑃𝑜𝑤𝑒𝑟(𝑊)]
10207
(8)
B.
Lithium Battery and Simulation Specific Calculations:
The capacity of a battery is taken to be:
capacity = voltage ∗ charge
(9)
where the capacity is the amount of energy in the battery measured in Joules and charge is the rated charge of the
battery measured in amp-hours.
The measured charges, voltages, and prices for many lithium-ion/poly batteries were taken from several online
retailers in order to determine a trend between these parameters and price. Initial inspection of a plot of price against
voltage shows a general positive trend. Unfortunately, as voltage increases the spread in price also increases. This is
logical as a high voltage cell is made of many lower voltage cells so the spread in price is expected to be multiplicative.
Figure 5. Price ($) vs. Voltage (V) for sampled batteries
Additionally, comparing a plot of price against charge also shows a general positive trend, with increasing spread.
Figure 6. Price ($) vs. Capacity (Ah) for sampled batteries
8|Page
Clearly then, the price is a function of both the charge and the voltage of the battery. Using the functions available on
ZunZun.com, a surface plot of a best fit curve was calculated. As seen below, the surface provides a good fit to the data
and illustrates the trend that price increases with both voltage and capacity.
Figure 7. Price vs. Voltage vs. Capacity for sampled batteries
A contour plot is also presented for clarity.
Figure 8.Capacity (Ah) vs. Voltage (V) for sampled batteries
9|Page
The result of this analysis yields the following equation to estimate the cost of a battery:
(10)
price ($) = 12.36 + 1.04 ∗ 𝑥 − 13.72 ∗ 𝑦 − 0.01 ∗ x 2 + 0.004 ∗ 𝑦 2
+ 0.002 ∗ 𝑥 3 − 0.02 ∗ 𝑦 3 + 1.93 ∗ 𝑥 ∗ y − 0.02 ∗ 𝑥 2
∗ 𝑦 + 0.02 ∗ 𝑥 ∗ 𝑦 2
In the equation above, x is the battery’s voltage and y is the battery’s charge measured in amp-hours.
C.
Weight and Simulation Specific Calculations:
For the purposes of this project, the lumped weight of a bicycle including all its components will be considered. Frame
material choices and quality of construction on all components of the bicycle will affect the overall weight. While we
are not including these considerations in our bike model, we are using the weight as a parameter as it will affect
requirements for motor power and battery capacity. In order to fully assess the tradeoffs of these components, a
generalization with weight will be considered so that we can determine the additional engineering and production
costs associated with weight reduction. The following plot was created using a sampling of road bikes.
Price ($) vs. Weight (lbs)
4000
y = 0.1333x4 - 16.408x3 + 747.95x2 - 14994x + 112408
R² = 0.8155
3500
Price ($)
3000
2500
2000
1500
1000
500
0
0
5
10
15
20
25
30
35
40
Weight (lbs)
Figure 9. Price ($) vs. Weight of Bike for sampled Bikes
This yields the fourth order polynomial fit for price against weight:
price ($) = 0.13 ∗ 𝑤 4 − 16.41 ∗ 𝑤 3 + 747.95 ∗ 𝑤 2 − 14994 ∗ 𝑤 + 112408
(11)
where w is the weight of the bike in pounds.
IV.
Task 4: Identify and Model the Remaining Relationships:
A.
Introduction:
Surveys were conducted to develop a demand model for the electric bike. Using price values from respondents for
bikes with various combinations of range, maximum grade, and weight, the demand and utility corresponding to any
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combination of these performance attributes (within defined ranges for each) can be determined. The following 20
figures are surface plots showing demand as a function of range and climbing ability and utility as a function of range
and climbing ability for 10 different bike mass values, ranging from 10 to 90 pounds.
B.
Obtained Graph:
From the excel file provided by the professor, we were able to obtain the following graphs:
Figure 10. Utility and Demand Graphs for bikes weight of 20 lbs
Figure 11. Utility and Demand Plot for bike weight of 28 lbs
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Figure 12. Utility and Demand Plot for bike weight of 36 lbs
Figure 13. Utility and Demand Plot for bike weight of 44 lbs
Figure 14. Utility and Demand Plot for bike weight of 52 lbs
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Figure 15. Utility and Demand Plot for bike weight of 60 lbs
Figure 16. Utility and Demand Plot for bike weight of 68 lbs
Figure 17. Utility and Demand Plot of weight of 76 lbs
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Figure 18. Utility and Demand Plot for bike of weight of 84 lbs
Figure 19. Utility and Demand Plot for bike of weight of 90 lbs
C.
Interpretation:
Overall, the demand function appears to make sense and provide reasonable values for utility and demand. In
general, each plot indicates an increase in demand or utility as one performance attribute is increased with the
other being held constant, which is expected. The demand plots do include local variations in which demand
decreases for increase in range and/or maximum grade, indicating the presence of a few irrational responses
among the survey data. Comparing successive plots as bike weight is increased, the overall utility and demand
values decrease, which also makes sense as consumers should be willing to pay more for a lighter bike than for a
heavier bike.
Please note that no other models were created. This is due to the belief that no additional model is needed at
this time.
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V.
Task 5: Integrate and validate your models:
The ebike model in Model Center is shown above and consists of five different components. The first Excel block
on the left is a variable generation block which allows the user to input the design variable changes, like a
specific battery or motor size, and get as output the corresponding resistance, inductance, and k value for the
emf, etc. This had to be used because changing the motor to the next size up or down changes basically three
variables that have to go to three different models. In one case, the value of battery capacity has to be
converted to different units for the Dymola models. The basic result of this block is an output that corresponds
to the design variables in blue on the left side of the modified influence diagram in Figure 1. The motor size, the
battery size, and the bike weight can be changed as parameters in this block and the corresponding variables
disperse to the other models to generate the e bike attributes; max climb angle, total ride distance, and the total
weight of the system.
The attributes that come out of the three midsection blocks in the Model Center model correspond to the green
attributes in the center of the influence diagram in Figure 1. The range model generates the overall range of the
configuration, while the grade model runs the simulation to determine the max achievable angle the ebike can
climb. The cost model takes in the motor, battery and weight input variables and estimates the total cost of the
ebike. This second level information then feeds into the demand spreadsheet where the demand is calculated
based on the attributes coming from the models and survey responses. From the combination of this demand
input, the attributes the overall utility is then calculated as a profit output. The model setup mirrors the
influence diagram in both function and in form. As more complexity is added when uncertainty is included, the
form will further branch incorporating more model elements.
From the Parametric studies done it was clear some of the elements were working as expected while others
were not. The mass varying study gave expected results in the attribute of range as can be seen in the below
figure.
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96000
94000
92000
90000
88000
RiderDistance
86000
84000
82000
80000
78000
76000
74000
72000
70000
68000
66000
64000
62000
15
20
25
30
35
40
Massin
RiderDistance
As the mass of the bike increases the overall distance the bike covers before the battery total discharges goes
down. In a similar fashion the max climb angle also decreases as the mass increase as can be seen in the figure
below.
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MaxAngle
0.455
0.45
0.445
0.44
0.435
0.43
0.425
0.42
0.415
0.41
0.405
0.4
0.395
0.39
0.385
0.38
0.375
0.37
0.365
0.36
0.355
0.35
0.345
0.34
0.335
0.33
15
20
25
30
35
40
Massin
MaxAngle
The next two figures show some odd results. Namely that as the weight goes up the utility goes up as displayed
in the next figure.
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750,000,000
700,000,000
650,000,000
600,000,000
550,000,000
500,000,000
Utility
450,000,000
400,000,000
350,000,000
300,000,000
250,000,000
200,000,000
150,000,000
100,000,000
50,000,000
0
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
Massin
Utility
This infinitely increasing profit trend is not what should be seen for this increasing weight of the bike. This result
needs to be investigated and addressed. The next Figure likely has an effect on the previous result because it
shows a decreasing trend as weight goes up, as would be expected to some degree, but it appears that the
equations in the cost model are getting inputs outside their meaningful range.
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18000.00
16000.00
14000.00
12000.00
10000.00
Cost
8000.00
6000.00
4000.00
2000.00
0.00
-2000.00
-4000.00
-6000.00
-8000.00
15
20
25
30
35
40
Massin
Cost
The next design variable that was modified was the battery size. This affects both the voltage and the capacity
of the battery. The expected result shown in the below figures corresponds to increasing battery size and
getting increased range.
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95789.5
95789.5
95789.5
95789.5
RiderDistance
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
95789.5
1
1.5
2
2.5
3
3.5
4
4.5
5
BatteryIn
RiderDistance
What is curious about this plot is that the graph looks right but the distances on the vertical axis all the same.
The assumption is that for the model there is a particularly steep hill at that point on the course and the rider is
unable to crest the hill cause the simulation to terminate. This will have to be addressed. In the next figure the
cost model seems to trend in the right direction but the values for cost are clearly too high.
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27460.00
27440.00
27420.00
27400.00
27380.00
27360.00
27340.00
27320.00
Cost
27300.00
27280.00
27260.00
27240.00
27220.00
27200.00
27180.00
27160.00
27140.00
27120.00
27100.00
27080.00
1
1.5
2
2.5
3
3.5
4
4.5
5
BatteryIn
Cost
It is believed that this is a result of an incorrect unit for weight going into the cost model. The cost analysis was
done in lbs. and the Dymola simulations are all in SI units. This problem should be easily fixed however we have
found that once Model Center has accessed the excel spread sheet it is occupied and not able to be modified
without shutting down the computer. Since a VPN connection had to be reestablished each time modifications
had to be done this became prohibitively time consuming and was abandoned until network access could be
better established. Both Utility and max climbing angle were both flat for this run. I believe the cost input to
the demand spreadsheet was out of reasonable range for or survey inputs.
For the next study the motor size was varied between the four motor sizes we investigated. Of the four variants
that were run only two produced plot points. The results mirror the results above. It is believed that the same
problems were occurring for both sets of runs.
The basic setup was successful and the benefit of Model Center can be clearly seen. More work needs to be
done to refine the Model Center model to make it more robust. The inconsistent results seem to be a mix of
model setup problems as well as some problems with unit consistency between models. Both will be resolved
before the next homework.
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7.5e+008
7e+008
6.5e+008
6e+008
5.5e+008
5e+008
4.5e+008
4e+008
3.5e+008
3e+008
2.5e+008
2e+008
1.5e+008
1e+008
5e+007
0
15
20
25
30
35
40
Massin
RiderDistance
VI.
MaxAngle
Cost
Utility
Task 6: Interpretation:
A.
Where did you struggle?
This assignment was especially challenging due to the fact that our simulation had to be working perfectly.
Refining the simulation to give realistic results was hard. We did however manage to overcome all obstacles. We
also struggled a bit on how to price our various parameters. Although we had initially used a simple linear
model, we decided to go back to our initial work to refine our model. This was partially due to the warning in the
assignment but also because of the fact that we were not getting satisfactory results.
There were considerable difficulties in learning the software and putting the system together in such a short
amount of time. Trying to watch the video lecture and work on model center proved difficult. What was more
troublesome was the inability to change individual models easily while debugging. This was a huge problem!
When modifying the Dymola model and rerunning a simulation to generated a new dsin file, the Model center
input file window would freeze and run very slowly, and delete a large number of lines. In two cases the
assigning of inputs had to be redone consuming significant numbers of time. These problems could be a result
of the hardware on which the program was being run. Not being able to debug and revise models was very
frustrating.
B.
Where did you go down the wrong path?
We had initially built a linear pricing model for our components. However because we did not think that it was
producing satisfactory results, we decided to go back and take a second look. Ultimately, we were able to come
up with satisfactory results using polynomials of various degrees.
C.
Did you learn anything new about the trade-offs in the system you were
designing?
We took a very long time, working on the pricing of the lithium batteries. Ultimately we learned that we should
not look simply at capacity but also at voltage to come up with an appropriate pricing system. Additionally, we
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were surprised to see the results that we obtained from the surveys. Although some results seemed surprising,
we decided to include all the surveys into our model. This was due to the fact that no survey was found to be
completely illogical.
VII. Task 7: Update Project Web-page
In addition to updating figures on the original portion of the project web page, new pages were added to include
the value models generated in this homework. The screen shot below shows the new Value Models landing page
that links to the cost and demand models generated. Each of these pages includes the graphs and figures
presented in this report as well as a brief description.
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VIII. Index Table of Figures:
Figure 1. Influence diagram for electric bike ......................................................................................................... 3
Figure 2. Top Level Broad Design ........................................................................................................................... 4
Figure 3. Means Network for Electronic Bike ........................................................................................................ 5
Figure 4 Price ($) vs. Power (B) of Motor for sampled Motors ............................................................................. 7
Figure 5. Price ($) vs. Voltage (V) for sampled batteries ...................................................................................... 8
Figure 6. Price ($) vs. Capacity (Ah) for sampled batteries .................................................................................. 8
Figure 7. Price vs. Voltage vs. Capacity for sampled batteries .............................................................................. 9
Figure 8.Capacity (Ah) vs. Voltage (V) for sampled batteries ............................................................................... 9
Figure 9. Price ($) vs. Weight of Bike for sampled Bikes .................................................................................... 10
Figure 10. Utility and Demand Graphs for bikes weight of 20 lbs ........................................................................... 11
Figure 11. Utility and Demand Plot for bike weight of 28 lbs .................................................................................. 11
Figure 12. Utility and Demand Plot for bike weight of 36 lbs .................................................................................. 12
Figure 13. Utility and Demand Plot for bike weight of 44 lbs .................................................................................. 12
Figure 14. Utility and Demand Plot for bike weight of 52 lbs .................................................................................. 12
Figure 15. Utility and Demand Plot for bike weight of 60 lbs .................................................................................. 13
Figure 16. Utility and Demand Plot for bike weight of 68 lbs .................................................................................. 13
Figure 17. Utility and Demand Plot of weight of 76 lbs ........................................................................................... 13
Figure 18. Utility and Demand Plot for bike of weight of 84 lbs .............................................................................. 14
Figure 19. Utility and Demand Plot for bike of weight of 90 lbs .............................................................................. 14
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