Hello and welcome to the session. In this session, we discuss the following question which says, a chemical industry produces two compounds C and D. The following table gives the units of ingredients P and Q per kg of compounds C and D as well as minimum requirements of P and Q and costs per kg of C and D. So, this table shows the units of ingredients P and Q presently compounds C and D. It also gives the cost per kg of the compounds C and D and also the minimum requirement of the ingredients in the compounds. And we have to find the quantities of C and D which would minimize the cost. Let's now proceed with the solution. Now as we are supposed to find the quantities of C and D, so for this we suppose let X kg of C and Y kg of D be produced. Now in this table we have as the minimum requirement of the ingredient P in the compounds C and D is 80. So, this means if we have X kg of C is being produced and ingredient P per kg in compound C is 1 unit. So, we have 1 into X that is X plus. Now as Y kg of B compound is being produced and ingredient P per kg in the compound D is 2 units. So, it would be 2Y. So, here we have X plus 2Y is the total ingredient P present in both the compounds C and D and this should be greater than equal to 80 as the minimum requirement of the ingredient P is 80. Now next we consider the ingredients Q. Now ingredient Q per kg present in compounds C is 3 units and in compound D is 1 unit and the minimum requirement of the ingredient Q in both the compounds is 70 units. So, here we have 3X plus Y should be greater than equal to 70. Now cost per kg of compound C is 4 dollars and of compound D is 6 dollars and as X kg of compound C is produced. So, which is the total cost of the X kg of the compound C produced. Now as 6 dollars is the cost of 1 kg of compound D and Y kg of compound D is produced. So, 6Y is the total cost of Y kg of the compound D produced and let this be equal to Z and this is the cost function. Now we have to find the quantities of C and D such that it would minimise the cost. So, we have to minimise Z equal to 4X plus 6Y to the constraints 2Y greater than equal to 80, 3X plus Y greater than equal to 70, X greater than equal to 0 and Y greater than equal to 0. These are the non-negative constraints. So, this is the problem that we are supposed to solve as this is the case of minimising the cost. So, we will use the isocost method for this. For this first of all we will find out the feasible region. So, the graphs of these constraints, before we start drawing a graph of these in equations we have to draw the graphs of the equations X plus 2Y equal to 80, 3X plus Y equal to 70, X equal to 0 and Y equal to 0. This is the line X plus 2Y equal to 80 and this is the line 3X plus Y equal to 70. Now X equal to 0 is the Y axis and Y equal to 0 is the X axis. Now next we will graph these constraints that is these in equations for this. We first consider the in equation X plus 2Y greater than equal to 80 and let's see if the 0.00 satisfies this in equation or not. On putting X equal to 0 and Y equal to 0 we get 0 is greater than equal to 80 which is not true and therefore we say that the 0.00 does not satisfy the in equation X plus 2Y greater than equal to 80 and hence the origin O does not lie in the region of X plus 2Y greater than equal to 80. So, the line X plus 2Y equal to 80 and the region to the right hand side of this line which does not contain the origin represents the region X plus 2Y greater than equal to 80 and this should be above the X axis and to the right of the Y axis because we have the non-negative constraints X greater than equal to 0 and Y greater than equal to 0. Next we consider the in equation 3X plus Y greater than equal to 70. Now putting X equal to 0 and Y equal to 0 in this we have 0 is greater than equal to 70 which is again not true therefore the point 0.00 does not satisfy the in equation 3X plus Y greater than equal to 70 and hence we can say that the origin O does not lie in the region 3X plus Y greater than equal to 70. So, the line 3X plus Y equal to 70 and the region to its right hand side but above the X axis and to the right of the Y axis would be the region that represents the in equation 3X plus Y greater than equal to 70. Also X greater than equal to 0 is above the X axis and Y greater than equal to 0 is to the right of the Y axis and so the region common to all these constraints is this shaded region that is the region A B C this shaded region is the feasible region. In the next step we will assign some constant value to the objective function Z. So, let the objective function Z equal to 4X plus 6Y be given a constant value say 100 then we get a line 4X plus 6Y equal to 100 or you can say 2X plus 3Y is equal to 15. Let this be equation 1 now we will draw a line p1 q1 to represent this equation 1. So, we have drawn this line p1 q1 representing this equation 1. In the same way we assign another constant value to the objective function Z. So, let objective function Z equal to 4X plus 6Y be given a constant value say 300. So, we get a line 4X plus 6Y is equal to 300 that is 2X plus 3Y is equal to 150. Now, let this be equation 2 and we will draw a line p2 q2 to represent this equation 2. This is the line p2 q2 which represents the equation 2 and this line p2 q2 is parallel to the line p1 q1. Now, as this constant value 100 is less than this constant value 300. So, we will move this line p2 q2 from p2 q2 to p1 q1 parallel to itself that is we will move the line p2 q2 in the decreasing direction towards the origin. So, that we obtain a line which is nearest to the origin and has at least one point common to the feasible region. Thus, we obtain a line p3 q3 which is nearest to the origin and passes to the point B of the feasible region. Now, as you can see this point B is the point of intersection of the lines 3X plus Y equal to 70 and X plus 2Y equal to 80. So, equal to 80 plus Y equal to 70 we get the value of X as and Y as 34. The point B has coordinates 12, 34 and so now we can say that we have a line p3 q3 which is to the origin the point B with coordinates 12, 34 feasible region. So, we can say that the optimal solution R X equal to 12 and Y equal to 34 the optimal value of your objective function Z equal to 4X plus 6Y is given as 4 into 12 plus 6 into 34 which is equal to 48 plus written 4 which is equal to 252. So, now the optimal value of the objective function Z is equal to 252 or we can say that Z is minimum at the point B with coordinates 12, 34 and hence we can say that for a minimum cost 12 kgs of 34 kgs of taken. So, this is our final answer. This coming is the session that we have understood the solution of this question.


What's good? Josh your boy Ross back again with another video. So you guys were requesting that I do a tier list of the pay-per-views from 2022 from WWE only on the main roster I'm gonna only keep it main roster cuz that's the pay-per-views that I pretty much watched I didn't watch too many NXT pay-per-views this year But I definitely watch pretty much all of the main roster pay-per-views. So you guys wanted it So I created a tier list and I wanted to pretty much put them in Respective tiers as I as I see fit This year for pay-per-views personally have been pretty good especially with Triple H taking over the pay-per-views at Triple H was pretty much In charge were pretty they were fantastic all of them for the most part have been Fantastic to watch and even the ones that Vince McMahon had been a part of and been the creative deciding factor there were some good ones there as well not every pay-per-view was stellar and And it must see but I feel like for the most part I don't think there was any pay-per-view this year that I was like this is just awful. This is bad This is this shouldn't have even happened I don't think I can say for this year and for the first time in a long time where there was a pay-per-view Where I was like you don't have a problem skipping I feel like there was something you can enjoy on each and every pay-per-view From 2022 this year from WWE and not just one match I want to say like at least two to three maybe even four matches or half the card You can somewhat enjoy and have a good time with and it's not a bad thing Even when Vince McMahon was in charge There was still a lot of good things on the show and there was also some misses but for the most part They knocked it out the party did pretty well this year pay-per-view wise So we're gonna get right into it, man Let's set this bad boy up man. Appreciate all love and support. Oh Man, I have a question. Yeah Are you tired of sitting in chairs that you feel like oh my back? bothering you Or the ones where the armrest doesn't get to the height that you wanted to Yeah, or the ones that don't rock back and forth like the rocking chair used to be in as a kid You see all that you see all that If that sounds like you guys Then what are you waiting for man? I need to get on down here to even racing. It makes you a chair right now down here I mean down to the website Yeah, man, these chairs are hella comfortable. We have to get some more This is not our first time getting some chairs from even racing shout out to you guys For definitely hitting us up about this and it's a product that we use on the day-to-day basis We finally had some more sent to us for the studio gaming set up and the home gaming set up So definitely we're proud to you know be able to let you guys know about this product man And the great thing is they're durable holds up to 400 pounds see they laughed at me when they see me jumping on the chair last time But yeah, you know you had to give it a tester and I that's it's it holds up to its work Yeah, 400 pound with no issue and they also have 4d chair armrests as well. Yeah, these armrests are Amazing especially when you're in those situations where a lot of times I found myself editing So it's good to have an armrest that I can adjust or when you're gaming and you're kind of locked in in the mold You know you can adjust it to your height of your gaming desk or whatever desk you're using and the quality on these are Top premier stitching leather. I love the pillows for the neck in the lower back Region so there'd be times where be gaming a lot or just editing videos and you know You want to be as comfortable as possible if you're sitting down for many many hours like we do when we're doing a live stream Yeah, man, and a couple of more things this they also have hub-less casters on this Which is pretty cool as well and also comparing this one to the XL chairs that they have When you think about height this one adjust to a pretty nice height where I actually keep your feet off the Actual I am man. My feet are dangling right now. You got taller than me. Oh, that's crazy, man. Yeah, watch this. Wait. Oh, yeah Just with ease with ease. Did you hear anything? Nope? Hey, I'm not gonna keep trying to sell you guys man You already know what to do man Make sure you go to the actual link that we have down below man It is our affiliate link you use the code clutch Yes, so make sure y'all go doing that right now man even racing every duty gaming chairs our top notch We wouldn't really be bragging about them this much if they weren't Yeah It's the perfect gift to give for Christmas and by clicking the link you support the channel as well Exactly man, so make sure you go get an e-ring game and racing chair right now You get more wins when you're comfortable while you're playing again But please hit you guys man and again. Thanks to you and racing facilities. Oh, thank y'all So all right, we're gonna start with which one we're gonna start with day one WWE day one day one for me Was it was it was okay? It wasn't that bad I think the highlight for WWE day one is The Seth Rollins Roman Reigns feud and Seth Rollins coming out there with the as this with the shield gimmick and Trying to get under Roman Reigns skinning for the first time in quite some time. We see Roman Reigns pretty much He just loses it man He intentionally this gets disqualified and it was a great match if the the atmosphere of WWE day one felt really big and honestly Even though, you know, there were some questionable booking decisions and stuff like that Bobby Lashley getting the win over Over a Brock Lesnar, you know, I wish they would have did that differently because you know That was a first-time match and they kind of really didn't go into great detail and really give chance Bobby Lashley a chance to really Seem like a credible threat to Brock Lesnar overall in general that pay-per-view I'm gonna go ahead and give it. I'm gonna give that a beat that was a beat level pay-per-view It wasn't bad. There were some things on there that was quite enjoyable. I'm gonna give that a beat All right, let's go to the Royal Rumble Now this one right here ladies and gents. This will probably put I think honestly This may be the lowest ranking pay-per-view on this show for for 2022 on my tier list It's gonna be the lowest ranking pay-per-view. I don't know why it's a show, but the Royal Rumble this year Especially the matches the men's and women's matches. I just I could care less I Honestly could care less when you had Rhonda Rousey come out there. I was like, all right. Well, Rhonda's winning this You know I'm saying like it just I was just I didn't care I didn't care especially what the men's would shame a man coming out there and doing what he did and trying to make himself the center point and then Brock Lesnar coming out There to win it. I Honestly, I didn't care. You're there to see who's gonna potentially main event WrestleMania. It just it was just so like It made me feel like damn, bro. What about the people that are actually there? What about the people that are there day in day out weekend win week out and and this is it didn't Hike me up for WrestleMania. I can tell you that much. This is probably one of those though It will be the lowest ranking tier for me I'm not I'm gonna have to put this I'm thinking I'm gonna go ahead and put this in I'm gonna give this a D, bro. Royal Rumble this year was not good, bro That's one that's one pay-per-view. I know full-fact. I will not go back and watch it was not that good It it wasn't I'm just be honest with you. So we're going with WrestleMania 38 this year I'm gonna group them together Because you know you got night one night two, but if I had to choose night one not gonna lie to you night one was Surprisingly really really well night one in my opinion was my favorite night. Night two was okay. It was not as bad I think the main event didn't live up to the height, but night one was Fantastic stone cold returning having an impromptu match Cody Rose coming back to one of the loudest ovations. We've seen in quite some time in WWE Outside of Bray Wyatt coming back to WWE that was amazing that match with Seth Rollins was amazing. Hell Logan Paul Showing out at WrestleMania this year was pretty good with his tag team match with the Miz going against the Mysterio I thought Mysterio's I thought that was good man overall night one was just great night two had some really great moments as Well, and if you had to group them together, this was a good WrestleMania this year.  That's an A. That's an A tier right there. That was a really good pay-per-view WrestleMania hasn't been that good in my opinion since damn near WrestleMania 31 That was like the last pay-per-view last time WrestleMania in my opinion has been very very good So I'm going with that one. Okay next one WrestleMania backlash. This is pretty much just rematches I ain't really care for it. I'ma I'ma give this a C the show. I mean It wasn't bad by any means, but once again, it was mostly rematches and they had some good matches on there for sure But I'm gonna give a go ahead and give this a C. It's it's it's kind of in the middle of the road it's not bad, but honestly, I mean If you saw WrestleMania you pretty much got a whole bunch of rematches and and and just It didn't I really wish they would get rid of the WrestleMania part and just stick with the backlash part I think I just gives it its own separate theme because we know backlash is traditionally WrestleMania rematches But you can spice up the feuds and it gives it that own identity. I don't like it's just basically WrestleMania extended. I don't I don't like that. I wish they would change the name of that But other than that, it's it's a C tier pay-per-view All right, I maybe ended up going out of order on some of these so that if I'm from the when they originally dropped so If that's the case, that's the case. All right, we're gonna do I Gotta do elimination chamber. I forgot to do elimination chamber because elimination chamber came before WrestleMania elimination chamber was okay. I think the most noticeable thing you can remember is Austin theory getting murdered That was a crazy thing him getting murdered from the top of the the sale by Brock Lesnar So, um, honestly, that's kind of it elimination was okay. I'm gonna give that a C tier That's a C tier right there. That's a C tier It wasn't anything that you know was just something that can go back and really watch other than the men's match But the men pretty much all got squashed by Brock. So I give that a C tier All right, let's get into money in the bank money in the bank I'm gonna go ahead and give that. I don't know. That's a tough one That's a that's a real tough one because money in the bank wasn't bad But I think the the decisions that were made kind of pitch people off Austin theory I know we were all wanting someone new and fresh, but I think giving Austin theory I don't have a problem with him winning it How he won it because he pretty much just got inserted at the last second and it kind of had people feeling some type of way Like it, you know, it definitely had some people kind of like I don't know what's going on here. Then you have to To me I feel like they kind of dropped the ball here Just booking wise especially Vince McMahon. I'm gonna go ahead and give this a C pay-per-view Just because of the outcomes Yes, Liv winning was cool. But at the same time when you really look back at it I'm okay with Liv winning, but I don't think she should have cashed in at night I think she should have possibly just held it out so they can extend it a little bit further and maybe Make that memorable moment from when she does cash in that more special.  Hell in a cell I'm gonna go ahead It was a good pay-per-view I'm gonna go ahead and give this one a B.  This was such a good match such a good feud You had a Seth Rollins trolling Cody Rhodes with the polka dots from his dad that his dad used to wear in his out on his outfits It was so great Cody Rhodes hitting the pedigree and hitting Seth Rollins with the sledgehammer was cool Also, Cody Rose getting hit with his own finishing rule crossovers. It was just it was so it was such a good match Anything that Cody did You felt the pain and he was feeling this is one of the first times in a long time when Cody took off his jacket People got quiet because they knew He's really hurt and he's about to wrestle in the hell in a cell match and this is People didn't know what to expect. This was one of the very few times Hell in a cell It lived up to his name and I think a lot of people gonna rate this paper view Really high just because of that match and I can't get mad at you. It's a beat here for sure All right, let's get into where things really started ramping up summer slam This was the last pay-per-view pretty much Vince McMahon had you know, pretty much set up everything in motion He wasn't there for that pay-per-view or triple H. It took over at this point, but The match had already been set the card had already been set Summer slam without a doubt is an A tier pay-per-view summer slam hadn't been this fun in quite some time like legitimately Fun the matches was good I want to say that is when Yeah Logan Paul this was his second match had a fantastic match with the men's at summer slam And of course probably one of the best last man standing matches ever and is he arguably in my opinion?  It was chaotic. I love this match. This is one of the best match This was each arguably their best match they've had outside of WrestleMania 31 Between Roman and Brock. This was fun. This was a it was a party for the summer. You had a Bailey coming back with Dakota Kai and EO And EO Shirai that that was a great moment Becky Lynch turning baby face It was so many good moments from this show It was really a party for the summer and summer slam hadn't been this good in quite some time as well So this was a good one and belongs in the eight here. All right, man We get into the nitty gritty now. We're getting to some of the best pay reviews of the year. I'ma go with I'm trying to try to maintain order So if I have to I'm gonna go clash at the castle, bro, that what are we talking about? It's a tear. I don't I don't even have to say anything clash at the castle is come. It's a tear It's one of the best shows WWE is put on all year. The crowd was amazing the matches. Most of the matches were fantastic edge teaming up with the Mysterio's take on Judgment Day fantastic Walter versus Sheamus match of the night fantastic crowd fantastic Seth Rollins Matt Riddle the lead-up was great the match was okay, but still enjoyable fantastic the main event One of the best matches Drew McIntyre Roman Reigns has ever had including that atmosphere fantastic, I Recommend those who haven't seen clash at the castle this year go watch it. It's up there It deserves to be there with WrestleMania and Summer Slam is here Great pay-per-view Great pay-per-view and once again shout out to the UK crowd you guys Showed up and showed out and I hope WWE makes this a tradition and comes back Overseas because y'all deserve all types of shows because you guys know how to You guys know how to turn up to a wrestling event and show up All right, so the next one we have extreme rules Honestly stream rules for the first time in a long time. They had some pretty things There was extreme stipulations or extremist stipulations, bro. I'm I'm gonna be honest with you Extreme rules was really really good. I'm putting this for the first time in a long time I'm putting this in the a category man extreme rules was great.  There was they actually had stipulations for matches and it made sense The fight pink could have been a little bit better But they made it a big deal.  We've gotten all year. It's Bray Wyatt returning a tier man a tier fun Fun pay-per-view extreme rules hasn't been fun and quite some time triple H was able to knock it out the park with this Right crown jewel Usually the crown jewels aren't that good with this one It's pretty goddamn good man. I'm gonna go ahead and give this a beat here man crown jewel was fun had some great matches on there and Like like we you know these Saudi shows sometimes take away and they don't really make sense in the grand scheme of things But I can appreciate this show because there were some good matches and I was entertaining I wasn't I wasn't bored throughout the show. I had a good time I'm going with crown jewel in the be tier category because it's it's something that honestly if you wanted to in my opinion I think it's probably the best crown jewel they've ever done Now a lot of people have said that it's the best crown jewel they've ever done So honestly, this is actually worth a rewatch. So I would definitely put that in a be tier category and the last one survivor series What are we talking about survivor series hasn't been this fun in my opinion since NXT was involved This was great in the fact that Triple H brought war games to survivor series It made you want to check it out. This wasn't about brand warfare It was just people going to war teams groups of people going to war with each other And it was fantastic and we got one of the greatest moments emotional moments Sami Zayn being embraced by J. Uso the bloodline Standing victorious. It was great future storylines was set up. This was fun This was ultimately fun war games made survivor series that more important and hopefully maybe this could be a tradition Maybe you have war games as survivor series as a tradition to skip it because that brand warfare stuff Let me cut that out because they only start to do that towards survivor series. No, I Think you should have war games as a yearly staple for survivor series just to give it that extra oomph and It seemed make it seem that important and it's cool to see One of the the major papers you finally get some relevance and love that is it is so rightfully deserved And that's my list man. We got WrestleMania here WrestleMania 38 as Tier a we got Summer Slam Clash at the Castle extreme rules and survivor series tier B day one hell in a cell crown jewel Tier C WrestleMania backlash Elimination chamber money in the bank and tier D Which is sad to say the Royal Rumble because that in my opinion was my least favorite pay-per-view for the outcomes And it just it did not hit like it was supposed to but yeah comment down below Let me know man. How do you guys rank these tiers as well? Let me know what not these tiers, but how you rank these pay-per-views What tiers would you guys put each one of these pay-per-views in man? Let me know. I really want to get your guys opinion on that And we can just have that discussion in the comment section, man But yeah this year has been pretty solid for some pay-per-views And I'm looking forward to what Triple H has to store for us for 2023 because I think he's gonna ramp it up even more Man, that's the one thing I can say the shows may not have been as good as we would have hoped them in a Triple H error for them the weekly shows but the PLE's or the pay-per-views whatever you want to call them They have been stellar and I love it and I'm looking forward to it So comment down below. Let me know how would you guys rank the pay-per-views for this year for 2022 on the main roster for WWE, but I appreciate all love and support row 250k appreciate y'all kicking with me. See you on the next one. Peace