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Q2: (7 points) Solve the following LP optimallyMaximize 2X1 5 X2 Subject - to. 2X+X2 < 5 XI - X2 <3 Xi <2 X/ 2 0 Xz unrestricted...

Question

Q2: (7 points) Solve the following LP optimallyMaximize 2X1 5 X2 Subject - to. 2X+X2 < 5 XI - X2 <3 Xi <2 X/ 2 0 Xz unrestricted

Q2: (7 points) Solve the following LP optimally Maximize 2X1 5 X2 Subject - to. 2X+X2 < 5 XI - X2 <3 Xi <2 X/ 2 0 Xz unrestricted



Answers

In Exercises $55-62,$ minimize or maximize each objective function subject to the constraints. Maximize $z=\frac{1}{4} x+\frac{2}{5} y$ subject to $$\begin{array}{rr}x+y \geq 5 & x+y \leq 7 \\-x+y \leq 5 & -x+y \geq 3\end{array}$$

Have you given you these inequalities here? One is this one is this. So just find out the corner points and then I used to find out maximize affect five explosive in white. So obviously brought a graph up here past too exposed to buy puts drill graph here you have four and 60, screw up every hand. Just go up next year. This line X plus Y plus five. So just wear a heavy hand +05 and fazio. So that's the graph. So now this is less than a cultural. So below region, less than equal five below region. So we have the system. I'm sorry. This is profitable region we have. This is the physical region. It's a corner points we have here at the corner points. The corner point is coming up to be 000. Next we have this point here that's coming out to 5:00. This point here coming out to visit a common pool. This point here we have not. Now, let's find out this point here. So this point is coming out to be So we have here two weeks plus three Y equals drill. And next we have X plus Y equals wife. So now let's here. We have uh two weeks plus three Y. Closed. Well one does point of intersection here and the next year because we're not doing it on the graph here. So just finding out the point of intersection here in texas, we have two weeks plus two white lady question to subtract here. So we have this coming out. Why equals true? So in a Y equals two. We just put it here. X equals three point is three comments. You know, if you just maximize this five, X was seven Y. The first point we have zero comma zero. Nor to maximize Next we have 5:00. Let's go for five, Commando. That'll be 25. Next 4,4.14 28 year we have next we have coming up to be 3:02. That gives now 15 plus 14 equals 29. So We have the maximum values committed 29 here, so 29. That's the maximum value. So we have not only nine hours maximum option one. Thank you.

Hello, everyone. Today we're going to start programs or fight required is to maximize exactly minus two it to square minus two X light minus three by two White Square plus X plus two way subject to the constraint express y minus five by two equals zero function if is equal to minus two X squared minus two Ex wife minus three by two y squared plus X plus too late and and fourth eggs. White Lander is equal to minus two X squared minus two. It's like minus three by two y square plus X plus two way plus Lambda indu X plus y minus five by two. So toe by toe executes zero. The FBI door wake was minus two. It's minus three wide plus two. Plus Lambda equals zero Doris Bye, Dolan. Because Express White, minus five by two, equals zero. You can write like on vehicles for X plus. No way minus line. Lambda equals to express three very minus two. So if it's all both off, that will get like X equals halfway minus one by two. Halfway minus half Bless like minus five by two equals zero. Figured y equals Don't X equals one day two into two minus half, which is half that. Send off a question. Thank you

We're trying to find the max or They is able to 2.5 x -3.1. Why? You're trying to find a maximum for this And we're told that X. It's great and equal to one. Why is less than or equal to 7? X. is also less than recalled to three and negative X. Plus. Why? He's great at night. You called to to also eggs plus. Why? It's great to be equal to 66 All right. So I can rewrite it for the constraints. X has to be greater than or equal to one and less than or equal to three. Let's just put it together like this. So that's one of the requirements. And uh having Z is equal to 2.5 X -3.1. Why? And um in order to do this to get the max, we need to have the biggest possible um X. Value and the smallest possible Y. Value. So what is the maximum value? X can be. Well, before we look into that, let's look into the values for Y. Because it has a bigger factor here. So one thing we can do over here is a look at the requirements that we have and try to find the constraint for why? What I mean is we have negative X. Us? Why? It's great gender equal to two. We also have eggs. That's why It's great. Yeah. You called to six. If we combined it to inequalities, you get to I He's created an import to eight or minimum value for why is four? It's a minimal value for why it's four. And um maximum value for X. Is three. But there's also this problem here to let me just put him over here. So I have one. His left hand is equal to X less than equal to three. And also have four. Is the senate equal to y. Let's enter equal to seven. Mhm. And what I need to do is to maximize X. And minimize why? But if I do that then X plus Y will be equal to seven. But I need to have X plus why? Um To be Last time a great Article 2 6 which it meets that requirement next I need negative eggs plus why? To be great and equal to two. My wife value has decided it's going to be negative three bus. My exile is gonna be -3. Uh It's gonna be three and negative X. Is gonna be negative three. Excuse me And my wife value is going to be four. That is gonna be one and that is not Great. Daniel Close to two. So what can we do? Uh The most logical thing to do here is two. Decrease the value of X. To something that would allow the requirement, meaning let X be too why not do that? But why why not increase increase? Why? Because it has a higher factor as we can see here? Okay, So let's plug it back in. My c. for max is going to be 2.5 Times 2 -3.1 times. For It's gonna be five minus 12.4, Giving us -7.4 forever max.

Hello, everyone. Today we're going to solve Cooper Number 29. Here we have to find X y and said that maximizes three x plus 55 plus zero dick with that minus Hector square minus lightsquared minus that square subject to constraints six minus X minus While minus that equals zero Function effect X Y Zed and Lambda is three x plus five y plus said minus eight square minus Y square minus eight square plus lamb Dyinto six minus X minus. Mine is set so the left by do it. Sequels three minus two x minus lambda Because zero draft, by the way, it was five minus. So why mine Islam die called zero the wife by those that because one minus does that minus lambda equals zero The left. But though Lambda it was six minus x minus Y minus that equals zero. So let this be equation. One toe, three full. So from one weekend, right, Like land Ike was three minus two weeks to we can write Lambda because five minus two y three lambda equals one minus two Set. This can be fight six Senate. Then on five and six, we can write three minus to Mexico's five minus two y X equals minus one plus y from six and seven. We can write like five minutes to y equals one minus. Does it? Is that because minus two plus white. So let it be eight and this can be mine. So from 89 and four, we can write, like six plus one minus lay minus lay plus two minus y equals zero. Why you called to three? Let it be Equation 10. Yeah. Then from eight, we can write like X equals two from my Enrique and I like that equals one. Let it be 11 and good. So X equals to do why he calls toe three. The articles one is the maximum value. That's the end of a question. Thank you.


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