List of top Mathematics Questions on Linear Programming Problem and its Mathematical Formulation asked in CBSE CLASS XII

Solve the following linear programming problem graphically: Maximise \( Z = x + 2y \) Subject to the constraints: \[ x - y \geq 0 \] \[ x - 2y \geq -2 \] \[ x \geq 0, \, y \geq 0 \]

The corner points of the feasible region of a Linear Programming Problem are $(0, 2)$, $(3, 0)$, $(6, 0)$, $(6, 8)$, and $(0, 5)$. If $Z = ax + by; \, (a, b>0)$ be the objective function, and maximum value of $Z$ is obtained at $(0, 2)$ and $(3, 0)$, then the relation between $a$ and $b$ is :

Solve the following Linear Programming Problem using graphical method : Maximize \( Z = 100x + 50y \) subject to the constraints \[ 3x + y \leq 600, \quad x + y \leq 300, \quad y \leq x + 200, \quad x \geq 0, \quad y \geq 0. \]

The corner points of the feasible region in graphical representation of a L.P.P. are \( (2, 72), (15, 20) \) and \( (40, 15) \). If \( Z = 1x + 9y \) be the objective function, then:

The feasible region of a linear programming problem with objective function \( Z = ax + by \), is bounded, then which of the following is correct?

Assertion : In a Linear Programming Problem, if the feasible region is empty, then the Linear Programming Problem has no solution.
Reason (R): A feasible region is defined as the region that satisfies all the constraints.

Solve the following linear programming problem graphically: Maximise \( Z = 20x + 30y \) Subject to the constraints: \[ x + y \leq 0, \quad 2x + 3y \geq 100, \quad x \geq 14, \quad y \geq 14. \]

For the given graph of a Linear Programming Problem, write all the constraints satisfying the given feasible region.

Solve the following Linear Programming Problem graphically:
Minimise \( Z = 3x + 5y \)
subject to the constraints: \[ x + 2y \geq 10, \quad x + y \geq 6, \quad 3x + y \geq 8, \quad x, y \geq 0. \]

Solve the following linear programming problem graphically: Maximise \[ Z = 2x + 3y \] Subject to the constraints: \[ x + y \leq 6 \] \[ x \geq 2 \] \[ y \leq 3 \] \[ x, y \geq 0 \]

Assertion (A): The corner points of the bounded feasible region of a L.P.P. are shown below. The maximum value of \( Z = x + 2y \) occurs at infinite points. 
Reason (R): The optimal solution of a LPP having bounded feasible region must occur at corner points. 

The maximum value of \( Z = 4x + y \) for a L.P.P. whose feasible region is given below is: