Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Linear Programming

Question:

Consider the LPP, with objective function optimize $Z=2x-y+5$ subject to constraints $3x+4y≤60; x+3y ≤ 30,x, y≥ 0$. If the corner points of feasible region are A(0,10), B(12, 6), C(20, 0) and O(0, 0), then

Match List I with List II

List I List II
A.  Minimum value of Z I.  45
B.  Maximum value of Z II.  50
C.  The sum of maximum and minimum value of Z III.  -5
D.  Maximum of Z - Minimum of Z IV.  40

Choose the correct answer from the options given below :

Options:

A-I, B-III, C-II, D-IV

A-II, B-III, C-IV, D-I

A-III, B-I, C-IV, D-II

A-IV, B-I, C-II, D-III

Correct Answer:

A-III, B-I, C-IV, D-II

Explanation:

$Z=2x-y+5$

points        value of Z
(0, 10)   -5 (minimum) = Zmin
(12, 6)   23
(20, 0)   45 (maximum) = Zmax
(0, 0)  

Zmax = 45, Zmin = -5

Zmax - Zmin = 50, Zmax + Zmin = 40

order A - III, B - I, C - IV, D - II