1 00:00:00,720 --> 00:00:03,460 Let's do some more practice of this concept. 2 00:00:03,810 --> 00:00:09,870 All right, say X and Y is given us ninety six and you need to maximize X plus. 3 00:00:10,590 --> 00:00:11,930 So what would be the case? 4 00:00:12,210 --> 00:00:16,320 What are all the possibilities in which I can write X and Y is ninety six. 5 00:00:19,240 --> 00:00:21,280 All right, these are all my possibilities. 6 00:00:21,440 --> 00:00:26,570 I can have one in the ninety six point forty three PRENDA thirty two or twenty four. 7 00:00:26,770 --> 00:00:32,440 I don't have five into something because I went to ninety six by five would give me ninety six, but 8 00:00:32,440 --> 00:00:34,490 nine to six by five is not an integer. 9 00:00:34,600 --> 00:00:39,370 All right, so over here we are taking the Kasmir X and Y has to be integers. 10 00:00:39,950 --> 00:00:40,340 All right. 11 00:00:40,510 --> 00:00:41,410 Now what about six. 12 00:00:41,500 --> 00:00:42,120 The 16. 13 00:00:42,130 --> 00:00:44,350 That's also nine, six, seven and two. 14 00:00:44,470 --> 00:00:47,550 Ninety six by seven is a ninety six. 15 00:00:47,770 --> 00:00:49,570 Ninety six by seven is not an integer. 16 00:00:49,570 --> 00:00:51,960 So we are not taking it and we have eight to 12. 17 00:00:52,270 --> 00:00:56,280 Now the next one after this would be well we do it right. 18 00:00:56,380 --> 00:00:57,850 So that's a repetition of this one. 19 00:00:57,850 --> 00:00:59,950 We don't take it and we stop at this point. 20 00:01:00,220 --> 00:01:03,850 Now in which case will X plus why be the maximum. 21 00:01:03,850 --> 00:01:04,170 Right. 22 00:01:04,300 --> 00:01:05,530 That's what we have to do. 23 00:01:05,830 --> 00:01:14,050 So you will find that when X and Y are kept as far apart as possible, you will get the maximum X plus. 24 00:01:14,470 --> 00:01:15,540 So that is over here. 25 00:01:15,760 --> 00:01:18,570 That's one plus ninety six, which is ninety seven. 26 00:01:18,850 --> 00:01:20,740 Now when would it be minimum. 27 00:01:20,890 --> 00:01:24,760 It would be minimum when you keep it as close as possible. 28 00:01:24,880 --> 00:01:25,220 Right. 29 00:01:25,600 --> 00:01:27,460 So that would be this case. 30 00:01:27,580 --> 00:01:30,730 That is eight plus twelve is equal to twenty. 31 00:01:31,030 --> 00:01:33,220 Now let's do one more example. 32 00:01:33,370 --> 00:01:39,250 Say X plus why he's given us twenty four and X and Y as to be integers. 33 00:01:40,710 --> 00:01:47,310 And you need to maximize the product and minimize the product to try it on your own before we do it 34 00:01:47,310 --> 00:01:47,790 together. 35 00:01:48,360 --> 00:01:49,710 All right, let's do it together. 36 00:01:49,920 --> 00:01:51,840 What are all the possibilities were? 37 00:01:52,080 --> 00:01:53,810 Plus, why is equal to twenty four. 38 00:01:54,300 --> 00:02:00,360 It can be one plus twenty three, two plus twenty two, three plus twenty one etc. up to twelve plus 39 00:02:00,360 --> 00:02:00,750 twelve. 40 00:02:00,750 --> 00:02:01,030 Right. 41 00:02:01,230 --> 00:02:03,270 Because beyond that, what would be the next one. 42 00:02:03,480 --> 00:02:06,150 It will be thirteen plus eleven. 43 00:02:06,180 --> 00:02:06,520 Right. 44 00:02:06,660 --> 00:02:09,540 And you will see that that's what would have been covered already. 45 00:02:09,540 --> 00:02:11,870 Here you have eleven over here and thirteen over here. 46 00:02:12,120 --> 00:02:13,080 So it's a repetition. 47 00:02:13,080 --> 00:02:16,170 So we stop at twelve, twelve right now. 48 00:02:16,170 --> 00:02:19,890 Among all of these when will X in Dubai be maximum. 49 00:02:20,130 --> 00:02:24,890 It will be maximum when you keep X and Y as close as possible. 50 00:02:25,050 --> 00:02:26,220 That would be over here. 51 00:02:26,460 --> 00:02:28,980 12 and 12 are the same number. 52 00:02:28,990 --> 00:02:30,470 So they are very close to each other. 53 00:02:30,600 --> 00:02:32,150 There is no distance between them. 54 00:02:32,460 --> 00:02:38,010 So twelve in the twelve is one forty four and that is the maximum X into right now. 55 00:02:38,010 --> 00:02:42,360 If you want to minimize, you need to keep X and Y as far apart as possible. 56 00:02:42,660 --> 00:02:46,200 But that's one in the twenty three which gives you twenty three.