Solve the following linear programming problem graphically:
Minimize : `z=3x+5y`
Subject to: `x+yge2`
`x+3yge3`
`xge0`
`yge0`

Explanation

First we draw the graph of the straight lines `x+y=2` and `x+3y=3`.
Now we find the feasible region from the constraints `x+yge2, x+3yge3,xge0,yge0` and shade it.

The vertices of this shaded region are `A(3,0), B(3/2,1/2)` and `C(0,2)`. We find the value of `Z` at these vertices.

Therefore at `x=3/2,y=1/2` minimum value of `Z` is 7.