Home
Class 12
MATHS
The minimum vlaue Z = 2x1 +3x2 subject...

The minimum vlaue ` Z = 2x_1 +3x_2` subject to the conditions `2x_1+7x_2ge22, x_1+x_2ge 6, 5x_1 +x_2 ge 10` and `x_1, x_2 ge 0 ` is

A

14

B

20

C

10

D

16

Text Solution

Verified by Experts

The correct Answer is:
A
Given, ` Z= 2x_1+3x_2`
` (##ARH_EGN_PRG_MAT_C17_E02_009_S01.png" width="80%">
The feasible region CABD is unbounded.
Thus minimum value of Z is 14, Here, fesible region is unbounded and the half plane , ` 2x_1+3x_2 lt 14 ` has no point in common with fessible region. So, required minimum vlaue of Z is 4.
Promotional Banner

Topper's Solved these Questions

  • Linear Programming

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|13 Videos

  • Linear Programming

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 1 (TOPICAL PROBLEMS )(Solution of LPP Graphical Method )|15 Videos

  • LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos

  • MATHEMATICAL LOGIC

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|22 Videos

Similar Questions

Explore conceptually related problems

The minimum value of z=2x_(1)+3x_(2) subjected to the constraints 2x_(1)+7x_(2)ge22,x_(1)+x_(2)ge6,5x_(1)+x_(2)ge10 and x_(1),x_(2)ge0 , is

The minimum value of 2x + 3y subject to the condition x+4y ge 8, 4x+y ge 12, x ge 0 and y ge 0 is

The point at which the minimum value of z = 8x + 12y subject to the constraints 2x +y ge 8, x + 2y ge 10 x ge 0, y ge 0 is obtained is

The minimum value of Z = 4x + 5y subjected to the constraints x + y ge 6, 5x + y ge 10 , x ge 0, y ge 0 is

By graphical method, the solutions of linear programming problem maximum Z = 3x_1 + 5x_2 subject to constraints 3x_1+2x_2 le 18 x_1 le 4, x_2 le 6,x_1 ge 0, x_2 ge 0

Maximize: Z = -x + 2y , subject to the constraints: x ge 3, x + y ge 5, x + 2y ge 6, y ge 0 .

Maximise Z= -x + 2y , subject to the constraints: x ge 3, x + y ge 5, x + 2y ge 6, y ge 0 .

Minimize z = -x_(1) + 2x_(2) Subject to -x_(1) + 3x_(2) le 10 x_(1) + x_(2) le 6 x_(1) - x_(2) le 2 and x_(1), x_(2) ge 0

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-Linear Programming -EXERCISE 2 (MISCELLANEOUS PROBLEMS )
  1. Consider the inequalities x1+x2 le 3,2x1+5x2ge 10x1,x2 ge 0 then feas...

    Text Solution

    |

  2. Z=4x+2y,4x+2y ge 46, x +3y le 24 and x and y are greater than or equ...

    Text Solution

    |

  3. The minimum vlaue Z = 2x1 +3x2 subject to the conditions 2x1+7x2ge22...

    Text Solution

    |

  4. The maximum value P = 3x + 4y subjected to the constraints x + y le 40...

    Text Solution

    |

  5. Consider the inequalities 5x1+4x2ge9,x1+x2 le 3, x1 ge 0 , x2 ge 0 Wh...

    Text Solution

    |

  6. The minimum and maximum values problem, of Z for the minimise and ma...

    Text Solution

    |

  7. The linear programming problem minimiseZ=3x+2y subject to the constrai...

    Text Solution

    |

  8. The maximum and minimum values of the objective function Z = x + 2y s...

    Text Solution

    |

  9. The maximum value of the objective function Z=3x+4y subject to th...

    Text Solution

    |

  10. Let x and y are the number of tables and chairs respectively, on which...

    Text Solution

    |

  11. The graphical solution of linear inequalities x+y ge 5 " and " x -y ...

    Text Solution

    |

  12. By graphical method, the solutions of linear programming problem maxim...

    Text Solution

    |

  13. A toy company manufactures two types of doll; a basic version doll; a ...

    Text Solution

    |

  14. The minimum value of Z = 10x + By subject to 4x +y ge 4, x +3y ge 6, ...

    Text Solution

    |

  15. The point which provides the solution of the solution to the linear pr...

    Text Solution

    |

  16. Shaded region is represented by , the constraints

    Text Solution

    |

  17. Let R be the feasible region (convex polygon) for a linear programming...

    Text Solution

    |

  18. The minimum value of the objective function Z=x+2y Subject to the c...

    Text Solution

    |

  19. Let the feasible region of the linear programming problem with the obj...

    Text Solution

    |

  20. The minimum and maximum values of the objective function, Z = 5x + 1...

    Text Solution

    |