plugin-hw02 - Assignment 2 Math 417 Winter 2009 Due January...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Assignment 2 Math 417 — Winter 2009 Due January 23 § 1.2#42. First, let’s assign variables for the traffic volume along each one of the four street segments marked with question marks. Let x 1 be the traffic on JFK St. between Winthrop and Mt. Auburn. Let x 2 be the traffic on Mt. Auburn St. between JFK and Dunster. Let x 3 be the traffic on Dunster St. between Winthrop and Mt. Auburn. Let x 4 be the traffic on Winthrop St. between Dunster and JFK. We use the convention that positive values for these variables indicates traffic flowing in the direction of the arrows, and negative values would indicate traffic flowing in the opposite direction (which is technically impossible since these are one-way streets). The cardinal rule of traffic is that all traffic flowing into an intersection must also come out of that intersection. This rule gives us one equation for each of the four intersections. JFK/Mt. Auburn: The inbound traffic volume is 300+ x 1 and the outbound traffic volume is 400 + x 2 , so we have the equation 300 + x 1 = 400 + x 2 . Mt. Auburn/Dunster: The inbound traffic volume is 100 + x 2 + x 3 and the outbound traffic volume is 250, so we have the equation 100 + x 2 + x 3 = 250 . Dunster/Winthrop: The inbound traffic volume is 120 + 150 and the outbound traffic volume is x 3 + x 4 , so we have the equation 120 + 150 = x 3 + x 4 . Winthrop/JFK: The inbound traffic volume is 300 + x 4 and the outbound traffic volume is 320 + x 1 , so we have the equation 300 + x 4 = 320 + x 1 . 1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Gathering these equations and rearranging in standard form, we find the system x 1 - x 2 = 100 x 2 + x 3 = 150 x 3 + x 4 = 270 x 1 - x 4 = - 20 The reduced echelon form of this system is x 1 - x 4 = - 20 x 2 - x 4 = - 120 x 3 + x 4 = 270 = 0 So the system is consistent and has infinitely many solutions, which are all of the form x 1 = - 20 + t, x 2 = - 120 + t, x 3 = 270 - t, x 4 = t, where t is an arbitrary parameter. However, not all of these solutions make sense since x 1 , x 2 , x 3 , x 4 must be nonnegative.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern