Let x and y hectare of land be allocated to crop A and B respectively. If Z is the profit then
Z =10500x + 9000 y …(i)
We have to maximize Z subject to the constraints
x + y ≤ 50 …(ii)
20x +10y ≤ 800 ⇒ 2x + y ≤ 80 …(iii)
x ≥ 0, y ≥ 0 …(iv)
The graph of system of inequalities (ii) to (iv) are drawn, which gives feasible region OABC with corner points O (0, 0), A (40, 0), B (30, 20) and C (0, 50).
Firstly, draw the graph of the line x + y = 50
Secondly, draw the graph of the line 2x + y = 80
Feasible region is bounded.
Now value of Z is calculated at corner point as
Corner Points |
Z = 10500x + 9000y |
O(0, 0) |
0 |
A(40, 0) |
420000 |
B(30, 20) |
495000 Maximum |
C(0, 50) |
450000 |
Hence the co-operative society of farmers will get the maximum profit of Rs. 4,95,000 by allocating 30 hectares for crop A and 20 hectares for crop B.
Yes, because excess use of herbicide can make drainage water poisonous and thus it harm the life of water living creature and wildlife.