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

Solve the following Linear Programming Problem graphically :
Minimize $Z = 20x + 10y$
subject to the constraints:
$x + 2y \le 40$
$3x + y \ge 30$
$4x + 3y \ge 60$
$x, y \ge 0$

In a linear programming problem, the feasible region representing the maximization of the objective function \( Z = px + qy \), where \( p, q > 0 \), is a shaded polygonal region. If all points on the line segment joining the corner points \( A(0, 3) \) and \( B(3, 2) \) give the maximum value of \( Z \), then which of the following is true?

Solve the following Linear Programming Problem graphically:
Maximize $Z = \frac{2x}{5} + \frac{3y}{10}$
subject to constraints:
$2x + y \le 1000$
$x + y \le 800$
$x, y \ge 0$.

Two statements are provided: an Assertion (A) and a Reason (R). Select the correct answer from the codes (A), (B), (C), and (D) given below: Assertion (A): Consider a Linear Programming Problem with minimise $Z = x + 2y$ subject to constraints $2x + y \geq 3$, $x + 2y \geq 6$, $x, y \geq 0$ which gives minimum $Z$ at infinitely many points. The corner points of feasible region are $(0, 3)$ and $(6, 0)$.
Reason (R): If two corner points produce the same minimum value of the objective function, then every point on the line segment joining the points will give the same minimum value.

The corner points of the feasible region determined by the system of linear constraints are \( (0, 0), (0, 40), (20, 40), (60, 20) \) and \( (60, 0) \). If the objective function of an LPP is \( Z = 4x + 3y \), then the maximum value is :

Solve the following Linear Programming Problem graphically :
Maximise $Z = 12x + 18y$
subject to the constraints \[ x + y \le 1200, \quad x - 2y \ge 0, \quad x + 3y \ge 600, \quad x \ge 0, \, y \ge 0 \]

Solve the following linear programming problem graphically: Maximize \( Z = 8000x + 12000y \) subject to the boundary constraints: \( 3x + 4y \le 60 \), \( x + 3y \le 30 \), with non-negativity restrictions \( x \ge 0, y \ge 0 \).

In a linear programming problem, the linear function which has to be maximized or minimized is called:

For a feasible region bounded by the corner points $(0,3)$, $(3,2)$, and $(5,0)$ in the first quadrant, the non-trivial constraints of the linear programming problem are:

Solve the following linear programming problem graphically:
Maximize \[ Z = 8000x + 12000y \] Subject to the constraints
\[ 3x + 4y \le 60 \] \[ x + 3y \le 30 \] \[ x \ge 0,\; y \ge 0 \]

In a linear programming problem, the linear function which has to be maximized or minimized is called