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Linear Programming
Question
Maximize z = 9 x + 3 y subject to the constraints
2x + 3y ≤ 13
2x + y ≤ 5
x, y ≥ 0
Solution
We have to maximize
z = 9x + 3 y
subject to the constraints
2x + 3 y ≤ 13
2x + y ≤ 5
x, y ≥ 0
Consider a set of rectangular cartesian axes OXY in the plane.
It is clear that any point which satisfies x ≥ 0,y ≥ 0 lies in the first quadrant.
Let us draw the graph of 2x + 3y = 13
For x = 0, 3y = 13 
For y = 0, 2x = 13 
Again we draw the graph of 2x + y = 5
For x = 0, y = 5
For y = 0, 2x = 5 
Since feasible region satisfies all the constraints.
OCEB in the feasibe region. The corner points are O(0, 0), 
At O(0, 0), z = 9(0) + 3(0) = 0+ 0 = 0
At 
At 
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