Find the Particular Solution Corresponding to the Tableau
For the following simplex tableau (a) Compute the next pivot lement: (b) Determine the next tableau: (c) Determine the particular solution corresponding to the tableau of part (b).(a) The pivot element is(b) Find the next tableau:[i4id4 Find the particular solution corresponding to the tableau in part (b): M=
For the following simplex tableau (a) Compute the next pivot lement: (b) Determine the next tableau: (c) Determine the particular solution corresponding to the tableau of part (b). (a) The pivot element is (b) Find the next tableau: [i4id4 Find the particular solution corresponding to the tableau in part (b): M=
Pivot once as indicated in each simplex tableau. Read the solution from the result.
$$
\begin{array}{rrrrrr|r}{x_{1}} & {x_{2}} & {x_{3}} & {s_{1}} & {s_{2}} & {s_{3}} & {z} \\ {4} & {2} & {3} & {1} & {0} & {0} & {0} & {22} \\ {2} & {2} & {5} & {0} & {1} & {0} & {0} & {28} \\ {1} & {3} & {2} & {0} & {0} & {1} & {0} & {45} \\ \hline-3 & {-2} & {-4} & {0} & {0} & {0} & {1} & {0}\end{array} ]
$$
So this section is primarily discussing slack variables and the pivot. And this is all part of linear programming using the simplest method. So for this problem that we're looking at, we are given the simplex tableau and we want to read the solution from the result. So given what we have, we have 22 31 00 0, 500 for one one 01 00 300. And then we have 7 to 4001 0, 700. And then lastly, we have negative three negative four negative. Two 00 zero. What? Zero. So we can transform this using row operations. Um, And when we transform it, we get it into this form right here. One three house one half 00 You're 2 15 30 negative. One half negative ones here. Zero 50. There we have 501 native one 010 200. And then we have 104 20 zero 1000. So, based on this, what we end up seeing is that if we have x one x two x three x four their side effects were s one s two n z This is going to equal zero Rx 10 Our x two we see is going to be 2. 15. Our X three is going to be zero R s. One is going to be zero Rs two is going to be 50 are s three is going to be 200 and Rs three is going to be 200 then our Z is going to be 1000. And let's recognize why that is. It's because we see these values are shared. So x one is zero. This is just by itself this one. So that means the X two corresponds to this right here. So it's 2 50 and then so on 00 this one right here just has the one in the calm. So it's going to correspond with 50. And then we have this one right here corresponds with 200 and then this one right here is the only one. So it corresponds with 1000
This time. Thank you. One, 21 10 on zero. Thank you, too. Negative one. Think it'll what? You know, So I mean it. Okay, The rest will just be like, were you 10 zero 01 There are 0010 on this one. Home. 50 engine. Yeah. What? They want us to pivot with choice. They want us to you on 103 it out. Let's just subtract from the top room. We'll end up with zero Mm. One. Yeah. Negative one here, then we can multiply by. Two is subtracted from the second row. 01 I 01 Negative, too. Zero number. We're leaving our pivot. Peru 10 10010 And now I'm multiplying by two to the bottom on it with their here. A negative one. Here, one here. Getting one here. 00 to those were multiple embedded. No one. Good. And now we'll have over here, I think. What's the basic solution here? Well, let's see. What is. Our BlackBerry will begin here, Lex. One is gonna be one of our basic variables. It's augmented value, uh, one being behind. All right. And that's all aware basic variables. Zero. Since we have only three country and there is the value of this, so are corresponding. Basic solution Near out zero zero four x two x three x one It's like wearable one. All right, variable too variable three. I really
It's time. Thank you. Blow you one three. Negative too. To one negative. One. 131 Negative. And then we have a slack variable. No, no, There uncle alone? No, they want us to pivot and then read off the corresponding basics. Well, it you want us to pivot using? Listen, but actually the variable X three columns That's one column that do you like that? We're gonna when we multiplied by three bottom? Well, one thing have in mind multiplied by three. My one, You're out. Actually, one zero zero and 45 minutes. And now we're gonna want for no one. Thank you. No one Europe. You have one one? Yeah, it is attracting from it. I need you here. Sounds like a final country. Well, multiply by three and then add to the work. Fine. Zero three euro. Yeah. One. 30. Okay, we can read off our basic solution from that. You're one. Value is there are new value. Zero for extreme value. First black variable value zero Somewhere we have a typo commission Still be a zero. So we actually have that Are seconds like variable. Yeah, nine on our third slack variables. A value of is this is that three Columns one and these A row or column with only one non zero well equipped them to their appropriate right hand side unlamented row.
This time they want us to pivot out givin tableau in the second calm here narrating calm because we want he really needing change at all. Okay, let me just write out, uh, whole tableau for him. One. Thank you, Heroes. You know, one there in a medicine track. Second. All right. It's new entries on the negative one here. Who was driving? They're out here. Three Here. One here. Negative. One year. You're out here. That's from some strengthening road from. Call him above it. No, I don't have to fight it out by two kidneys. Units here it of the column Blue one one one in in their ass. Now I could multiply by three and add it to the bottom. We'll get a zero here. Well, the plan by three and out into the bottom. So I get that you're here well defined by three. Adding to the bottom and I'll get negative 1/2 here. The negative 3/2. This one I mean zero. It'll be a negative 3/2. This isn't a call on the industry. I remember that Will remain is the one Multiply my great. Solicit the negative so we can read off our solution. Well, this is the X two column three and then slack states here. Zero we have to Constraints was going to be to non zero century extra. Only has one none. Zero injury. It's gonna be equal to the ah glints of column on the right. Yes. One only have the one. There are injuries. The arguments in column on the right. Think our solution will be zero Europe for exit sting for us one zero for us in the value of negative. All right.
3 answers
Let u(€,t) satisfy the PDEutt 4uct for € € Rand t > 0.(a) Write down the expression for the characteristic € X+(t) emanating from = = 4 att = 0.X+(t)(b) Supposeu(z,0) = 3cos(c ~ 4)andut (1,0) = 6sin(c _ 4) Then u(22,9)Number(c) Now, suppose u(c,0) = 3sin(x 4) and u+ (1,0) = 0.2(4,9)
Let u(€,t) satisfy the PDE utt 4uct for € € Rand t > 0. (a) Write down the expression for the characteristic € X+(t) emanating from = = 4 att = 0. X+(t) (b) Suppose u(z,0) = 3cos(c ~ 4) and ut (1,0) = 6sin(c _ 4) Then u(22,9) Number (c) Now, suppose u(c,0) = 3sin(x 4) and...
Find the Particular Solution Corresponding to the Tableau
Source: https://itprospt.com/num/2071403/for-the-following-simplex-tableau-a-compute-the-next-pivot