Sponsor Area
Linear Programming
Find the maximum value of f = x + 2 y subject to the constraints:
2x + 3 y ≤ 6
x + 4 y ≤ 4
x, y ≥ 0
We are to maximize
f = x + 2y
subject to the constraints
2x + 3 y ≤ 6
x + 4 y ≤ 4
x, y ≥ 0
Consider a set of rectangular cartesian axes OXY in the plane.
It is clear that any point which satisfies x ≥ 0, y ≥ 0 lies in the first quadrant.
Now we draw the graph of the line 2 x + 3 y = 6.
For x = 0, 3 y = 6, or y = 2
For y = 0, 2 x = 6, or x = 3
∴ line meets OX in A (3, 0) and OY in L (0, 2)
Let us draw the graph of line x + 4 y = 4
For x = 0, 4 y = 4, or y = 1
For y = 0, x = 4
∴ line meets OX in B (4, 0) and OY in M (0, 1)
Since feasible region is the region which satisfies all the constraints
∴ OACM is the feasible region. The comer points are
At 
Some More Questions From Linear Programming Chapter
Solve the following Linear Programming Problems graphically:
Maximise Z = 3x + 2y
subject to the constraints: x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0,
Maximize z = 4x + 1y such that x + 2y ≤ 20, x + y ≤ 15, x ≥ 0, y ≥ 0.
Minimize z = 2x + 3y, such that 1 ≤ x + 2y ≤ 10, x ≥ 0, y ≥ 0.
Solve the following linear programming problem graphically:
Minimise Z = 200x + 500y
subject to the constraints x + 2y ≥ 10, 3x + 4 y ≤ 24, x ≥ 0, y ≥ 0
Solve 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
Minimise and Maximise Z = 3x + 9y
subject to the constraints:
x + 3y ≤ 60
x + y ≥ 10
x ≤ y
x ≥ 0, y ≥ 0
Show that the minimum of Z occurs at more than two points.
Minimise and Maximise Z = 5x + 10y subject to constraints x + 2y ≤ 120, x + y ≥ 60, x - 2 y ≥ 0, x, y ≥ 0.
Minimize z = 5x + 7y such that 2x + y ≥ 8, x + 2y ≥ 10, x, y ≥ 0.
Sponsor Area
Mock Test Series
Mock Test Series