UGTRB MATHS-2026 UNIT-9 CLASS-7 #tutorflicks #dualsimplexmethod #primalanddual #duality #ugtrbmaths

Added: 2026-06-01

[00:00:01]Welcome to tutor flicks.

[00:00:08]Hi teachers duality.

[00:00:21]So duality programming problem max same solution exist programming problem.

[00:00:59]Okay.

[00:01:03]Same solution.

[00:01:07]Okay.

[00:01:09]Okay.

[00:01:13]First question max.

[00:01:31]Okay. Maximize minimize it.

[00:01:43]Max.

[00:01:45]Okay.

[00:01:46]Max number of variables.

[00:01:54]Number of constraints.

[00:01:58]Okay. So, number of variables.

[00:02:09]Okay.

[00:02:11]number of constraints.

[00:02:17]Number of variables.

[00:02:21]Okay.

[00:02:24]X1, X2, X3.

[00:02:27]Okay.

[00:02:34]So number of variables next less than or equal to x1 + y2 greater than or equal to 5 x1 + 2 y2 less oral less thanal x1 y2 unrestricted. Okay.

[00:03:37]X1 X2 X1 X2 greater than or equal to X1 X2 unrestricted.

[00:03:52]Okay.

[00:04:01]Next in the primintrainte.

[00:04:22]Okay. Next coefficient of objective function right hand side objective function function right next I variable in the conraint to constraints x1 x2 x2.

[00:05:02]Okay.

[00:05:11]First max is ital.

[00:05:17]Okay. Next subjectal.

[00:05:25]Okay.

[00:05:27]Maximum.

[00:05:38]Okay.

[00:05:42]Maxum.

[00:05:46]Next.

[00:05:51]right handic 2x + y greater than or equal to 6 5 y uh sorry 5 x + 7 y= minimum is star = 6 x + 7 ypose.

[00:06:40]Okay.

[00:06:42]Next, subject to the constraints.

[00:07:07]Next.

[00:07:09]Maximum subject to the constraints x1 x2 x1 xal function greater than or equal to function. Next.

[00:07:45]Okay.

[00:07:48]problem.

[00:07:50]Maximum is = 5x + 4 y + 2 subject to the conraints variable greater than or equal to maximum.

[00:08:07]Next question right next to the constraints 1 2 3 1 2 3 1 2 3 Okay, Next step plus 2 1 2 1 2 Okay.

[00:09:01]Okay.

[00:09:04]x + 2 y 2 x + y 3 x + 2 y and then less thanal. Okay.

[00:09:23]Okay.

[00:09:28]Okay.

[00:09:34]The problem maximum right hand functionic column Right.

[00:10:09]Maxive function right hand.

[00:10:18]So 5 4 minimize is it equal to cx subject to the constraint ax X greater than or equal to B X= 0 max.

[00:10:55]Next Apose Xal.

[00:11:15]Nextp objective function objective function right handal variable nonative restrictions.

[00:11:44]Soal.

[00:11:57]Okay.

[00:12:02]So duality max right.

[00:12:28]Okay.

[00:12:29]A x + y a b ysal greater than or equal to greater than equal to.

[00:12:53]Okay. So first unrestricted.

[00:13:08]Okay.

[00:13:14]Next dual simplex method. Dual simplex method.

[00:13:30]So simplex standparing for subject to the constraints oral right Standard form simp. Okay.

[00:14:07]Okay.

[00:14:13]less than or equal to simpalus less than=us problem Right hand side.

[00:14:48]Okay. Right hand side.

[00:14:57]Okay.

[00:15:15]minimize max.

[00:15:23]Next.

[00:15:31]Okay.

[00:15:33]Max subject to the constraints.

[00:15:47]Okay.

[00:15:49]Max S1, S2, S3 S1, 0 S2, 0 S3. The max 0 s1 + 0 s2 plus 0 s3 or equal to conditionality.

[00:16:26]variable.

[00:16:30]Max simpal and right hand side greater than or equal to Z.

[00:16:53]Current solution is an optimum feasible solution. Okay.

[00:17:02]S1 = -3. S2 = -6. S3 = 3 initial basic feasible solution in solutional right hand side initial solution solution. Okay.

[00:17:53]Next.

[00:17:55]Okay. and entering variable leaving next.

[00:18:08]Okay.

[00:18:10]Simply ratio ratio positive value least. Simp 5 - 6 - 4 0 ratio 5 6 elegative values ratio.

[00:19:39]positive values.

[00:19:51]Okay.

[00:19:54]Simplex ratio least positive simplex.

[00:20:08]is a minus c least positive ratio most negative. Okay.

[00:20:32]variable simpitive values least positive value or equal to Current solution. Optimum solution.

[00:21:20]Okay.

[00:21:26]Next. Duality. Duality.

[00:21:29]The dual of the dual is. Okay. So okay again max Next we duality theorem xible solution in case x less than or equal to transpose solution. Okay. X W X Y sorry Wasable solution C or equal to B transpose W in the conditions.

[00:23:00]Okay, next fundamental theorem of duality optimum solution.

[00:23:14]Okayum solution optimum solution. Okay, next feeasible solution solution.

[00:23:54]imum solution.

[00:24:03]Okay. Next unbounded solution.

[00:24:16]Okay.

[00:24:19]unbounded solution.

[00:24:22]No feasible solution.

[00:24:25]Next integer programming problem. Linear programming problem.

[00:24:30]Integer programming problem.

[00:24:35]X12 decision variables. Decision variables.

[00:24:45]Negative values.

[00:24:48]Okay. So in case Just pure IP pure integer programming problem X1 X2 pure integer programming problem IP X1 X2 IP 01 IP 01 IP X1 X2 X3 and program 01 integer programming problem. Okay.

[00:26:19]So, linear programming problem.

[00:26:25]Okay.

[00:26:46]programming problem.

[00:27:03]G E N O R Y in our book. G O M O R So, branch and bound method additive method, generalized penalty fund simp and bound.

[00:27:59]branch and bone x1 x2 x3um solution.

[00:28:11]Next traveling salesman problem. Okay.

[00:28:18]Traveling salesman problem.

[00:28:24]Okay.

[00:28:27]Programming problem.

[00:28:37]Programming problem.

[00:28:45]First introduction class.

[00:28:48]Solutions generate and degenerate and non degenerate degenerate non degenerate degenerate x1 x2 x3 decision variable nonenerate non Okay.

[00:29:29]So types of solution simplex graphical next two dual simplex. Next IP next transportation problem simplex.

[00:29:57]Okay. Revised simplex table is it same minus CJ format.

[00:30:27]So simple% programming problem.

[00:30:53]Thank you.