subject to constrains: 1.5x + 3y = 42 .......(1) 13x + y =24 .........(2) x and y greater than 0.
Answers
Step-by-step explanation:
Question 1:
Maximize Z = 3x + 4y
Subject to the constraints: x + y ≤ 4, x ≥ 0, y ≥ 0
Answer:
The feasible region determined by the constraints x + y ≤ 4, x ≥ 0, y ≥ 0 is as follows:
Class_12_Maths_Linear_Programming_Figure1
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:
Class_12_Maths_Linear_Programming_Table1
Therefore, the maximum value of Z is 16 at the point B (0, 4).
Question 2:
Minimize Z = −3x + 4y
subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0
Answer:
The feasible region determined by the system of constraints x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0
is as follows:
Class_12_Maths_Linear_Programming_Graph1
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:
Class_12_Maths_Linear_Programming_Table2
Therefore, the minimum value of Z is −12 at the point (4, 0).
Question 3:
Maximize Z = 5x + 3y
subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0
Answer:
The feasible region determined by the system of constraints 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0,
and y ≥ 0, are as follows:
Class_12_Maths_Linear_Programming_Graph3
The corner points of the feasible region are O (0, 0), A (2, 0), B (0, 3), and C (20/19, 45/19).
The values of Z at these corner points are as follows:
Class_12_Maths_Linear_Programming_Table3