Long Answer TypeSolve the following problem graphically:
Minimise and Maximise Z = 3x + 9y
subject to the constraints:
x + 3y ≤ 60
x + y ≥ 10
x ≤ y
x ≥ 0, y ≥ 0
Solve the following linear programming problem graphically:
Minimise Z = 3x + 5y subject to the constraints:x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0
We are to maximise
Z = - x + 2 y subject to constraints x ≥ 3, x + y ≥ 5, x + 2 y ≥ 6, y ≥ 0.
y = 0 is x-axis.
So y ≥ 0 represents region on and above x-axis.
Now x = 3 is a straight line AL parallel to y-axis at a distance 3.
Now we draw the graph of x + y = 5
For x = 0, y - 5
For y = 0, x = 5
∴ line meets OX in B(5, 0) and OY in M(0, 5).
Again we draw the graph of x + 2y = 6.
For x = 0, 2y = 6 or y = 3
For y = 0, x = 6
∴ line meets OX in C(6, 0) and OY in N(0, 3).
Since feasible region satisfies all the constraints.
∴ shaded region is the feasible region, which is unbounded.
The comer points are C(6, 0), D(4, 1), E(3, 2).
At C(6, 0), Z = - 6 + 0 = - 6
At D(4, 1), Z = - 4 + 2 = - 2
At E(3, 2), Z = - 3 + 4 = 1
∴ greatest value of Z is 1 at (3, 2).
Since feasible region is unbounded.
∴ we are to check whether this value is maximum.
For this, we draw the graph of - x + 2y > 1 ...(1)
Since (1) has common points with the feasible region.
∴ Z has no maximum value.
Switch
