Solve the following problem graphically:Minimise and Maximise `Z = 3x + 9y` . . . (1)subject to the constraints: `x+3ylt=60` . . . (2) `x+ygeq10` . . . (3) `xlt=y` . . . (4) `xgeq0,ygeq0` . . . (5)

Explanation

Let `Z=3x+9y`....(1)
Converting inequalities to equalities `x+3y=60` to solve these equation we get the required points are `(0,20),(60,0)`
`x+y=10` we get required points are `(0,10),(10,0)`
and `x−y=0` we get required points are `(0,0),(10,10),(20,20)`
Plot the graph for the set of points
The graph shows the bounded feasible region. `ABCD`, with corner points `A=(10,0),B=(5,5),C=(15,15)` and `D=(0,20)`To find maximum and minimum
`[["Corner point",|,Z=3x+9y],[A=(0,10),|,90],[B=(5,5),|,60],[C=(15,15),|,180],[D=(0,20),|,180]]`
From the graph maximum value of X occurs at two corner points `C(15,5)` and `D(0,20)` with value 180 and minimum occurs at point `B(5,5)` with value `60.`