exercise -12.1 sol: myncertsolutions
TRANSCRIPT
Exercise -12.1
Q1: Maximize Z = 3x + 4y
Subject to the constraints: x + y :S 4, 0 :S x, 0 :Sy
Sol:
The feasible region determined by the constraints, x + y � 4, x <? 0, y <? 0, is as
follows:
y
6
2
x·
{O,o>° X
x+y:a:4
Y'
The corner points of the feasible region are O (0, 0), A (4, 0), and B (0, 4).
The values of Z at these points are as follows :
Corner point
0 (0, 0)
A ( 4, 0)
B ( 0,4)
Z = 3x + 4y
0
12
16 ⇒Maximum
Therefore, the maximum value of Z is 16 at the point B (0, 4).
Q2: Minimize Z = -3x + 4y subject to x +2y :S 8, 3x +2y :S 12, x 2: 0, y 2: 0.
Sol:
The feasible region determined by the system of constraints, x +2y :S 8, 3x
+2y :S 12, x 2: 0, y 2: 0 is as follows:
y
Y' 3x+ 2v�12
The corner points of the feasible region are O (0, 0), A (4, 0), B (2, 3), and C
(0, 4). The values of Z at these corner points are as follows.
Corner point Z =- 3x + 4y
NCERT SOLUTIONS CLASS-XII MATHS CHAPTER- 12
LINEAR PROGRAMMING
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