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Hello Everyone,
I am new to the forum, but I am kind of at a loss and I could use a little guidance. I currently have an assignment where we are given a traffic circle, with 4 on ramps and 4 off ramps (labeled a through h) which are constants. We are then given the traffic flow in between each of the on and off ramps as variables x1 through x8. None of the constants or variables are given an actual value (we are supposed to treat these as real numbers).
We are supposed to analyze the traffic circle, create a system of equations in order to solve for the values of x1 through x8 (the traffic flow) and analyze the constraints of the constants (a through h  on/off ramps) and the values of x1 through x8.
I have a diagram of the traffic circle, with the on/off ramps and sections of the circle labeled with the appropriate variables and constants (including work I have done so far) in the attached PDF (sorry for the horrible handwriting).
Normally when given a problem like this, we are least given some data to work with, in order to find the values of the variables, but since we are given no data (just that the constants are a through h and that they mark the different on / off ramps) i'm just a little confused as to how to solve this. I started by creating a system of equations regarding the constants and the variables we were given, then tried to solve the system of equations in order to get values for x1 through x8, now I am just stuck.
I am unsure if I even created the correct system of equations for this problem, and if I did, did I solve the system correctly?
I am not asking for someone to give me the direct answer to the problem, but any assistance in helping me with this problem could really help.
Please give me your opinions on what I have done so far, and if I did anything wrong, please let me know what.
Thank You
I am new to the forum, but I am kind of at a loss and I could use a little guidance. I currently have an assignment where we are given a traffic circle, with 4 on ramps and 4 off ramps (labeled a through h) which are constants. We are then given the traffic flow in between each of the on and off ramps as variables x1 through x8. None of the constants or variables are given an actual value (we are supposed to treat these as real numbers).
We are supposed to analyze the traffic circle, create a system of equations in order to solve for the values of x1 through x8 (the traffic flow) and analyze the constraints of the constants (a through h  on/off ramps) and the values of x1 through x8.
I have a diagram of the traffic circle, with the on/off ramps and sections of the circle labeled with the appropriate variables and constants (including work I have done so far) in the attached PDF (sorry for the horrible handwriting).
Normally when given a problem like this, we are least given some data to work with, in order to find the values of the variables, but since we are given no data (just that the constants are a through h and that they mark the different on / off ramps) i'm just a little confused as to how to solve this. I started by creating a system of equations regarding the constants and the variables we were given, then tried to solve the system of equations in order to get values for x1 through x8, now I am just stuck.
I am unsure if I even created the correct system of equations for this problem, and if I did, did I solve the system correctly?
I am not asking for someone to give me the direct answer to the problem, but any assistance in helping me with this problem could really help.
Please give me your opinions on what I have done so far, and if I did anything wrong, please let me know what.
Thank You
Homework Statement
Homework Equations
The Attempt at a Solution
Attachments

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