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Solve the Following Linear Programming P...

Solve the Following Linear Programming Problem graphically : Maximise `Z = 3x + 4y` subject to the constraints : `x+ylt=4,xgeq0,ygeq0`.

A

`16`

B

`18`

C

`20`

D

`14`

Text Solution

Verified by Experts

The correct Answer is:
A
Draw the graph of equation `x+y=4`.
Now obtain the feasible region for the inequalities `x+yle4, xge0, yge0`. The convex region is `OAB` whose are `O(0,0),A(4,0)` and `B(0,4)`. Now we will find the value of `z=3x+4y` at each vertex.


Therefore at `x=0, y=4,z` is maximum and the maximum value is `16.`
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