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00:00 - 00:59 | maximize Z is equal to 8 x + 9 Y subject to constrain given below 2 X + 3 Y equal to 3 X - 2y less than equal to say and Y equal to 1 X and Y greater than zero given that two equations to 1 + 3 Y less than or equal to 1 and 3 x minus 2 Y equal to sec and also given that why is less than equal to 13 question and equations with 21 will convert them in equations first become 2 X + 3 Y is equal to 3 x minus 2 Y is equals to check now will calculate the point so that employ these equations on graph when you put x is equals to zero y comes out to be true |

01:00 - 01:59 | in the preferred Y is equal to zero X comes out to be 34 equation 2 X + 3 Y equal to 6 and for their 3 x minus 2 if we put x is equal to zero y comes out to be 3 and minus 3 any support Y is equals to zero X comes out to be too and we have Y is equal point r02 and 30 for equation 2 X + 3 Y equal and equation x minus 2 Y is equal to 6 the points are 0 - 3 and 20 Kendra come 0 1 Chu 3 Airtel come one |

02:00 - 02:59 | Tu Shri -1 -2 minor - 1 - 2 - 3 points for 2 X + 3 Y equal to sec r02 that is 1 0 and white 2 and 3 2019 will be from this point Tu because it is given that x and y are greater than 0 so we will be taking just the positive side now line 3 x minus 2 Y is equal to 6.0 - 3 that is zero and Y - 3 and |

03:00 - 03:59 | 20 that is access to and y09 will be like this man will be from hair from this point to point extend this point now kab se shading part always check whether the line will cover area towards the origin or from away from the region by check GIT add origin will take X and Y is equal to zero X and Y in the equation if we put the row Into X + 3 Y is satisfy the equation if its equation that we will shade towards the origin and if it does not satisfy the equation |

04:00 - 04:59 | we will shade away from origin as in all the cases it will satisfy the equation if we put X and Y is equal to zero so we will shade the region which is near to the nation that desi point can be a free intersection hair d and now we need to maximize Z is equal to 8 x + 9 Y but we need points CNC also to check whether where the value of a where the value of that is maximum the point is the intersection of line y is equals to 1 and 2 X + 3 |

05:00 - 05:59 | Y we will be calculating it by so we calculate interest by elimination method 2 X + 3 Y is equals to say and Y is equals to 1 if the value of 1 in the above equation we get X is equals Re Y2 the point comes out to be 3 by 2 comma 1 this is point by point C is the intersection of lines 2 X + 3 Y is equal to 6 and 3 x minus 2 Y equal to that 2 X + 3 Y is equal to take and 3 x minus 2 Y is equal to 6 now we will try elimination method and calculate the values of X and Y 4 x + 6 Y is equals to |

06:00 - 06:59 | 12 and 9 x minus 6 Y is equal to 18 x this equation with to this equation with three so that we can cancel out six vi easy 13 x equals to 30 and value of x comes out to be 30 by 13 and substituting the value of Egg we find out why which comes out 613 so h t point is 3013 comma 6:30 now we will check at which point the value of that is maximum Corner Point Corner Point and value red Qualis 28 x + 9 y when we take point a that is |

07:00 - 07:59 | 010 the value of Z comes out to be if you could act as one and why every row value comes out to be a if we put if it 1 point 3 by 2 1 the value that comes out to be 21 and if we put value as 30 by 13 and 65 13 the value of Z comes out to be 294 by 13 and it will take 2.20 values it comes out to be 16 now we can really see the value of Z is maximum at 4.30 13 and 6:30 so the maximum value of Z is 29413 |

08:00 - 08:59 | at point 30 by 30 36 30 |

**Introduction**

**Linear programming problems**

**Some definition**

**Mathematical Formulation of Linear programing problem(Example)**

**Optimal Product line problem**

**Diet Problem**

**Transportation problem**

**Feasible solution In feasible solution Feasible region in feasible region**

**Convex set and extreme point value theorem**

**Corner point method**