List of top Mathematics Questions on Linear Programmig Problem asked in CBSE CLASS XII

Solve the following linear programming problem graphically: Maximise \( Z = 2x + 3y \), subject to the constraints: \( x + y \leq 6, \, x \geq 2, \, y \geq 3, \, x \geq 0, \, y \geq 0. \)

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. 
 

Graph Content

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

Graph for region
(b) Evaluate: \[ \int_{1}^{3} \left(|x - 1| + |x - 2| + |x - 3|\right) \, dx. \]
A linear programming problem deals with the optimization of a/an:
If \( A = \begin{bmatrix} 1 & -2 & 0 \\ 2 & -1 & -1 \\ 0 & -2 & 1 \end{bmatrix} \), find \( A^{-1} \) and use it to solve the following system of equations:

\[ x - 2y = 10, \quad 2x - y - z = 8, \quad -2y + z = 7. \]