Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Intersections in England are often constructed as one-way "roundabouts," such as the one shown in the figure. Assume that traffic must travel in the directions shown. Find the general solution of the network flow. Find the smallest possible value for $x_{6} .$figure can't copy

The general solution$\left\{\begin{array}{c}{x_{1}=100+x_{6}} \\ {x_{2}=x_{6}} \\ {x_{3}=50+x_{6}} \\ {x_{4}=-70+x_{6}} \\ {x_{5}=80+x_{6}} \\ {x_{6} \text { is free }}\end{array}\right.$

Since $x_{4}$ cannot be negative, the minimum value of $x_{6}$ is $70 .$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 6

Applications of Linear Systems

Introduction to Matrices

McMaster University

Harvey Mudd College

Lectures

01:32

In mathematics, the absolu…

01:11

11:48

Find the general flow patt…

12:42

a. Find the general traffi…

02:46

Solve each problem.The…

00:43

The figure at the top of t…

07:29

The figure shows the inter…

07:04

Refer to Exercises 83 and …

01:26

The figure for Exercises 2…

19:24

Determine the values of x1…

06:41

Traffic Flow A section of …

01:24

The following problem was …

Okay, So in this problem, we need to find out the find the general solution of the network flow. And here we have six intersections that it's a B C D E f, and we need to counter flow in and blow out. Okay, so for Intersection A, we have X one closing on next to does 100 blowout. And for Intersection B, we have X two plus 50 No win and next three goes out. Now we're into section C. Where have X three blows in and X four. That's 100 and 20 no out into second D Explore and 1 50 slow win and x five goes out or into section E. We have X five close in and X six bus. Hey, t blowout! They're in two sections. Have we have X six last 100? No win and X one flow out. Okay, so all these expression should be equal. And so based on our table here, we can write down corresponding matrix. So noticed that this should be a six by should be a six by seven matrix. So excuse me. No, that's the note column, SPI X one X two X tree Teoh X six for bye six. And for the first for the first roll, we have one neck of one and other article you visions will be zeros. And the council term, it's 100 for the second row. We have one for a X to neck of one breaks three and other other terms are all zeros. So on the cast in terms next 50 and their role similar T constant term is 1 20 and fourth row would be one negative one and constant term is negative 1 50 and they throw one next one and 80 The last rule we have connected one or x one and one for X x six and accounts in terms of connective 100. So all in terms, art zeros. So here's our metrics. Now we need to apply gushing gushing elimination. Uh huh. Scuse me, um, to get to get the reduce station for me. So in this case, I would just just write it down. So it is 11 111 We have five ones and zero, and these terms will be next one Next one. Next one, Next one. So we have five negative ones, and it's all Jews. And the last last column we have under zero 50 connective 17 Amy and New. Okay, so based on our reduced Asian of form, you know that X one minus x six is It is 100 and next to minus X six is zero x three minus x six iss 50 Next four minus next six is note 20 and x five. My list six is 80 and next six is pre variable. All right, so we stopped the first question. Now the second question is to find the smallest possible battle for X six. So in this case, um, we need to find XXXIX as small as possible, but noticed that ax to is Symantec's six. If we take XX as that's my password, that C zero, the next to will be zero and the rest the resident. The rest of variables will be x one is 100 x two zero x three 15 x four Connected 20 and x five 80 now Excuse me. So we don't allow negative number for for the flow because now we have we take x x six as zero. Then export will be next 20. This this is impossible. So in order to make a and this non active a negative X War. So we need X six to be at least, um, Daddy's we need to make exit X four minus x six, because next 20 your ex for is negative 20 last x six. So, Dad means we need to make X six minus 20 bigger or equal to zero because export cannot be cannot be negative. So that means X six minus 20 should be bigger. Only 06 you going to 20. So put in for the from the mean minimum of six, we can take xx to be 20. This this is our final solution for the minimum xx we can take and we're not.

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, the absolute value or modulus |x| of a real number x is its …

Find the general flow pattern of the network shown in the figure. Assuming t…

a. Find the general traffic pattern in the freeway network shown in the figu…

Solve each problem.The figure shows four one-way streets with intersecti…

The figure at the top of the next page shows two intersections labeled $\mat…

The figure shows the intersections of four one-way streets.a. Set up a s…

Refer to Exercises 83 and 84 in Section 7.3 The figure shows four one-way st…

The figure for Exercises 29–32 shows the intersections of three one-way stre…

Determine the values of x1, x2, x3, x4 for the following traffic flow diagra…

Traffic Flow A section of a city's street network is shown inthe fi…

The following problem was posed on National Public Radio’s Weekend Edition: …

02:27

Let $S : \mathbb{R}^{p} \rightarrow \mathbb{R}^{n}$ and $T : \mathbb{R}^{n} …

02:40

In Exercises $25-28$ , determine if the specified linear transformation is (…

02:52

Verify the uniqueness of $A$ in Theorem $10 .$ Let $T : \mathbb{R}^{n} \righ…

02:24

Could a set of three vectors in $\mathbb{R}^{4}$ span all of $\mathbb{R}^{4}…

03:13

One serving of Post Shredded Wheat® supplies 160 calories, 5 g of protein, 6…

09:09

In Exercises $1-6,$ solve the equation $A \mathbf{x}=\mathbf{b}$ by using th…

02:28

Use the inverse found in Exercise 3 to solve the system$8 x_{1}+5 x_{2}=…

05:10

Find $A^{-1}$ as in Exercise $17,$ using $A$ from Exercise 3

01:52

Let $A$ be a $6 \times 5$ matrix. What must $a$ and $b$ be in order to defin…

03:28

Compute the determinants in Exercises $1-8$ using a cofactor expansion acros…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.