Home
Class 12
MATHS
Maximum value of Z = 12x + 3y subject t...

Maximum value of Z = 12x + 3y subject to constraints ` x ge 0,y ge 0, x+y le 5 ` and ` 3x+y le 9` is

A

15

B

36

C

60

D

40

Text Solution

Verified by Experts

The correct Answer is:
B
Given constraints are ` x ge 0, y ge 0, x+y le 5 ` and ` 3x+ y le 9.`
Objective fucntion max Z= 12x +3y
Here, feasible region is OABCO.
` (##ARH_EGN_PRG_MAT_C17_E01_038_S01.png" width="80%">
At point O (0, 0), Z = 12 (0) + 3(0) = 0
At point A (3, 0), Z = 12(3) + 3(0) = 36
At point B (2, 3), Z = 12(2) + 3(3) = 33
At point C (0, 5), Z = 12(0) + 3(5) = 15
Hence, maximum "'.alue of Z is 36
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • Linear Programming

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2 (MISCELLANEOUS PROBLEMS )|30 Videos

  • 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 MHT CET Corner|13 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

Maximum value of Z = 3x + 4y subject to the constraints x + y le 4, x ge 0, y ge 0 is 16.

State True or False: The maximum value of Z = 5x + 3y subject to constraints 3x + y le 12, 2x + 3y le 18, 0 le x ,y is 20.

Knowledge Check

  • Maximum value of 12x + 3y subject to constraints x ge 0, y ge 0, x + y le 5 and 3x + y le 9 is

    A
    15
    B
    36
    C
    60
    D
    40

  • The maximum value of z = 10x + 6y subject to constraints x ge 0, y ge 0, x +y le 12, 2x +y le 20 is

    A
    72
    B
    80
    C
    104
    D
    110

  • Maximum of P=5x+3y subject to the constraints: x ge 0, y ge 0, 5x+2y le 10 is

    A
    6
    B
    10
    C
    15
    D
    25

    • Similar Questions

    Explore conceptually related problems

    Find maximum value of z=2x+3y subject to the constraints x+y le 4 , x ge 0 , y ge 0 .

    The maximum value of Z= 10x+6y subject to constraints x ge 0, y ge0, x+y le 12, 2x+y le 20 , is

    The maximum value of Z = 3x + 5y subjected to the constraints x + y le 2, 4x + 3y le 12, x ge 0, y ge 0 is

    The point at which the maximum value of Z = 4x + 6y subject to the constraints 3x + 2y le 12, x + y ge 4, x ge 0, y ge 0 is obtained at the point

    The maximum value P = 3x + 4y subjected to the constraints x + y le 40, x + 2y le 60, x ge 0 and y ge 0 is

    Home
    Profile