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Use the simplex method to solve the following maximum problem: Maximize: 401 523Subject to the constraints:Tt + %2 < 10 311 712 <42 20 22 > 0and using vour...

Question

Use the simplex method to solve the following maximum problem: Maximize: 401 523Subject to the constraints:Tt + %2 < 10 311 712 <42 20 22 > 0and using vour final tableau answer the questions below bv entering the correct answer in each blank box: Please_enter fractions %5 3/5, E4LZ,endsq.on.

Use the simplex method to solve the following maximum problem: Maximize: 401 523 Subject to the constraints: Tt + %2 < 10 311 712 <42 20 22 > 0 and using vour final tableau answer the questions below bv entering the correct answer in each blank box: Please_enter fractions %5 3/5, E4LZ,endsq.on.



Answers

Use the simplex method to solve each linear programming problem.
$\begin{array}{ll}{\text { Maximize }} & {z=5 x_{1}+2 x_{2}} \\ {\text { subject to: }} & {2 x_{1}+4 x_{2} \leq 15} \\ {} & {3 x_{1}+x_{2} \leq 10} \\ {\text { with }} & {x_{1} \geq 0, \quad x_{2} \geq 0}\end{array}$

Time they ask us Farm the simplest mother My maximization problem. This is the corresponding initial tablet one easy monetary and now we're gonna pivot. We're gonna get you most negative home on. Let's look at the ratios with EOG Mons. Good. Call him. No. When you find one three, so one is 25 1 is only five. We're definitely gonna choose the sentry. And here is what I get. All right. Pavlos might differ by a scale for each row, but that's OK. Uh, aimed to get a zero here and zero here in row one. Okay, a 10 zero three negative. One zero in row three A 10 here my 75. And we see that we have all positive entries. So we have found our maximum to our original problem. Um, let's see if I can interpret that base our basic very after. Yet you? Yeah, three ass one is equal to Is he crazy? So are corresponding. Basic solution should be zero fine. 20 zero on the value of 75. Sounds reasonable. Ah, I forgot to 75 see, divided by three. So we'll end up with a value of 20. I got

So they give us a maximum. I have turned into the following tableau, and I'm going to be selecting the largest cone the most negative. Comb this for the indicating and then I'm going to choose from the ratios. 21 times 5/17 are 11 times 50 Okay, so the top is a bit bigger song. I didn't choose this engine right here on my goal will be to eliminate slit eye zeros here and here. So when I do that without an Jiro Operations, I will end up with 7/5 here. Zero on 11/5 years, a negative 17/5 here, zero on a 44/5 year. The room eliminating from can remains him on the foot. The 1 29 over here at zero here. Zero here, 21/5 here in a loving over five here, Syria 31/5. Now our tableaus might different by scaler is on the rose. But that's okay. They're equivalent another in a military operation. But notice all of these indicators are positive, so we can now terminate. That's just interpret our solutions. Right now we have 11/5 X two is equal to 11 and we have 11/5 s. One is equal to 44/5 and that are value chewed at this point. Claims to 31/5. So the corresponding basic solution will be zero on that. Seeing want to play a vibe over 11 5 supply for here months. He are slack variable to is just zero on this on the right iss Well, what's to 31? Divided by 11? Don't have that in my random access memory. Let's see. I can break it down. Probably 21. Yeah. Subject. So 21 this is a resolution attains the value.

So this time they he's ization problem which turned into a and with my traces, these in the pit variable. Now, intermediates ups might differ by a scaler. That's okay, That's an element. Your operate CNN and choose the most negative on that will be the column. Now, let's look at the ratio of money over to the 24 over to you. Okay, so, 10 I'm gonna choose this entry, pivot all the others. The goal will be to make, um zero you hear in here. So let's see. You know, from an honored your operation dull to this row. All end up. Where s zero negative? One to zero 0 80 I'll end up with negative for here. Zero negative too. 0 to 0. He and on the bottom will end up with positive 28 0 12 That looks good. 00 You 2 40 So we can terminate. We found our Max because all of these entries positive We can increase their value anymore. Let's see, we have two X two is equal to 20. We have Teoh. This one we have to s three is equal. Teoh 80. We have, uh but is us too and we have Teoh three and I have to z is equal toe party. Our basic solution converting those will be a 10 zero 40 four with the value of 120.

In this problem. Translator maximization in the temple. You're so zero funny. Well, one for negative. Far, only ever Slack variable here. Is he here? Yeah. Normally, we would choose the most negative. But, you see, we would have to abandon all coms. We shouldn't have a negative denominator. And so we kind of have for going to proceed so we could try that. So smallest ratio, this one's 25. This one. Let's change the on. Let's want his ear out. The other selections, add it to the bottom row. Will have negative nine. Well, uh, zero one, one. Well, okay. And, uh, for the top, you can multiply by four. Practice from, so we'll have zero negative. 17. Okay. Looking self here. Why? Well, next up, this one is going to be our only negative, uh, indicator. And well, both of these are negative. So we actually went must be shoes. This as our private home because we can choose x two and make it more negative. All our options are negative. And that actually corresponds as we saw the text being unbounded and our solution no maximum exists. We hang Ah, as negative. We can just in creep increasing our function as much as we want were a choice the next two years.


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