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Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 43
Answers (1)
Answer: The society will get the maximum profit of Rs.495000 by allocating 30 hectares for crop X and 20 hectare for Crop y.
Hint:
Let x hectare of land be allocated to crop x and y hectare to crop y.
Given:
Profit per hectare on crop x=Rs.10500
Profit per hectare on crop y = Rs.9000
Solution:
By the given profit on x crop and y crop.
Total profit=Rs.(10500x+9000y)
The mathematical formulation of the problem is as follows.
Maximize Z = 10500x + 9000y
Subject to the constraints
(Constraint related to land) … (i)
(Constraint related to use of herbicide) i.e
… (ii)
(Non –negative constraint) … (iii)
Let us draw the graph of the system of inequalities (i) to (iii).
The feasible region ABC is shown (shaded)
|
Corner Points |
Z=10500x+9000y |
|
O(0,0) |
0 |
|
A(40,0) |
420000 |
|
B(30,20) |
495000(Maximum) |
|
C(0,50) |
450000 |
The coordinate of the corner points O, A, B and C are (0,0), (45,0),(30,20) and (0,50) respectively.
Let us evaluate the objection function Z = 10500x + 9000y at these vertices to find on gives the maximum profit.
Hence, the society will get the maximum profit of Rs.495000 by allocating 90 hectares for crop x and 20 hectares for crop y.
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