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Maximise Z=3x+4y Subject to the constr...

Maximise `Z=3x+4y`
Subject to the constraints
`x+yle4,xge0,yge0`

Text Solution

Verified by Experts

First we draw the graph of the line `x+y=4`.
Now we find the feasible region from `x+yle4, xge0,yge0` and shade it. The vertices of this region are `O(0,0),A(4,0)` and `B(0,4)`. At each vertex, we find the value of `Z=3x+4y`.

There at `x=0, y=4` the maximum value of `Z` is 16.
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Knowledge Check

  • Solve the Following Linear Programming Problem graphically: Maximise Z=3x+4y subject to the constraints : x+y =0,y>=0

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