Home
Class 12
MATHS
The maximum and minimum values of the ob...

The maximum and minimum values of the objective function Z = 3x - 4 y subject to the constraints
`x- 2y le 0, -3x +y le 4 `
` x-y le 6 , x,y ge 0`
are respectively

A

12,10

B

10,12

C

12,-16

D

5,12

Text Solution

Verified by Experts

The correct Answer is:
C
Given , objective funciton
Z = 3x-4y .
Subject to the constraints are
` x- 2y le 0 `
`-3x +y le 4 `
` x -y le 6 `
`x, y ge 0 `

The feasible region which is unbounded is AOB and the carmer points are ` O(0,0) , A(0,4), B(12,6)`

Thus, maximum value and minimum value of Z are 12 and -16 respectively. Here, feasible region is unbounded and the half plane determined by `3x -4y gt 12 ` and `3x - 4y lt -16` have no point in common with the feasible region so maximum and minimum values of Z are 2 and 6 respectively
Promotional Banner

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

The maximum value of the objective function Z=3x+4y subject to the constraints x+y le 4, x ge 0 , y le o is

The minimum and maximum values of the objective function, Z = 5x + 10y subject to the constraints x +2yle 120, x+y ge 60, x -2y ge 0 , x,y le 0 are respectively

The maximum and minimum values of the objective function Z = x + 2y subject to the constraints x+2y ge 100, 2x -y le 0, 2x +y le 200 occurs respectively at

Minimize Z = -3x + 4y subject ot constraints : x + 2y le 8, 3x + 2y le 12, x ge 0, y ge 0 .

Maximize : Z = x + y ,subject to the constraints: x - y le -1, -x + y le 0, x ge 0, y ge 0

Maximize z = 5x + 10y subject to constraints x + 2y le 10 , 3x + y le 12 , x ge 0 , y ge 0

Find the ratio of the maximum and minimum values of the objective function f=3x+5y subject to the constraints : x ge 0, y ge0, 2x+3y ge 6 and 9x+ 10y le 90 .

Maximize z =2x + 3y subject to constraints x + 4y le 8, 3x + 2y le 14 , x ge 0, y ge 0 .