Let `x` passengers are of executive class and `y` passengers are of economy class.
Maximise `Z=1000x+600y`……………1
and constraints `x+yle200`………………2
`xge20`…………….3
`y-4xge0impliesyge4x`…………..4
`xge0,yge0`............5
First draw the graph of the line `x+y=200`.
Put `(0,0)` in the inequation `x+yle200`,
`0+0le200implies0le200`. (True)
Thus, half plane contains the origin.
Now, draw the graph of line `y=4x`
Put `(10,0)` in the inequation `yge4x`,
`0ge4xx10implies0ge40` (False)
Thus, half plane will be opposite to `(10,0)`.
Now draw the graph of line `x=20`
Put `(0,0)` in the inequation `xge0,0ge20` (False)
Thus, the half plane does not contain origin.
Since `x,yge0`, So the feasible region will be in first quadrant.
From the equations the points of intersection are `A(20,80),B(40,160)` and `C(20,180)`.
`:.` Feasible region is ABCA
The vertices of the feasible region are `A(20,80),B(40,160)` and `C(20,180)` at which we find the value of `Z`.
Thus, the maximum value of `Z` is 136000 at point `B(40,160)`. Therefore, maximum cost is Rs. 136000 for which 40 tickets of executive class and 160 tickets of economy class are required.