Solve the following Linear Programming Problem graphically :
Minimise `Z = x + 2y` subject to
`3x+ygeq3,x+2ygeq6.x ,ygeq0`.

Explanation

Minimize `Z = x + 2y`
subject to
` " " "3x+ygeq3`,
` " " " x+2ygeq6`
` " " " x ,ygeq0`






Since, the region that is feasible is unbounded, so 6 may or may not be minimum value of `Z`

We need to graph inequality


There is no common point between feasible region & inequality
`therefore Z=6` is minimum on all points joining line `(0,3), (6,0)`
i.e. `Z=6` will be minimum on `x+2y=6`

Explanation- Taking points on line `x+2y=6`


Hence, `Z` is minimum at all points joining `(0,3), (6,0)`
`Rightarrow Z` will be minimum on all points joining line `(0,3), (6,0)`
`therefore Z` will be minimum on `x+2y=6`