Solve the following linear programming problem graphically: Maximise `Z" "=" "4x" "+y` . . . (1) subject to the constraints: `x+ylt=50` . . .(2) `3x+ylt=90` . . .(3) `xgeq0,""""ygeq0` . . .(4)

Explanation

the feasible region determine by the system of constraints (ii) to (iv) . we observed that feasible region `OABC` is bounded so we now use corner pint method to determine the maximum vale of z . the coordinate of the corner points `O,A,B` and C are `(0,0), (30,0),(20,30)` and `(0,50)` respectively .Now we evaluate Z at each corner point
`[["Corner point",|,Z=4x+y],[A=(0,0),|,0],[B=(30,0),|,120],[C=(20,30),|,110],[D=(0,50),|,50]]`
Hence
maximum value of z is 120 at the point `(30,0)`