Let x and y be number of A and B trees.
∴According to the question,
20x + 25y ≤ 1400, 10x + 20y ≤ 1000, x ≥ 0, y ≥ 0
Maximize Z = 40x + 60y
The feasible region determined by 20x + 25y ≤ 1400, 10x + 20y ≤ 1000, x ≥ 0, y ≥ 0 is given by
The corner points of feasible region are A(0,0) , B(0,50) , C(20,40), D(70,0).
The value of Z at corner points are
Corner Point |
Z = 40x + 60y |
|
A(0, 0) |
0 |
|
B(0, 50) |
3000 |
|
C(20, 40) |
3200 |
Maximum |
D(70, 0) |
2800 |
|
The maximum value of Z is 3200 at point (20,40).
Hence, the man should plant 20 A trees and 40 B trees to make maximum profit of Rs.3200