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

Solve the following linear programming problem graphically: \[ \text{Minimise } Z = 2x + y \] subject to the constraints: \[ 3x + y \geq 9, \] \[ x + y \geq 7, \] \[ x + 2y \geq 8, \] \[ x, y \geq 0. \]
In a Linear Programming Problem, the objective function $Z = 5x + 4y$ needs to be maximised under constraints $3x + y \leq 6$, $x \leq 1$, $x \geq 0$, $y \geq 0$. Express the LPP on the graph and shade the feasible region, and mark the corner points.
Consider the Linear Programming Problem, where the objective function \[ Z = x + 4y \] needs to be minimized subject to the following constraints: \[ 2x + y \geq 1000, \] \[ x + 2y \geq 800, \] \[ x \geq 0, \quad y \geq 0. \] Draw a neat graph of the feasible region and find the minimum value of $Z$.

For a Linear Programming Problem, find min \( Z = 5x + 3y \) (where \( Z \) is the objective function) for the feasible region shaded in the given figure.

In a Linear Programming Problem (LPP), the objective function $Z = 2x + 5y$ is to be maximized under the following constraints:

\[ x + y \leq 4, \quad 3x + 3y \geq 18, \quad x, y \geq 0. \] Study the graph and select the correct option.

For a Linear Programming Problem (LPP), the given objective function is $Z = x + 2y$. The feasible region PQRS determined by the set of constraints is shown as a shaded region in the graph.

The point $P = ( \frac{3}{13}, \frac{24}{13} )$, $Q = ( \frac{3}{15}, \frac{15}{4} )$, $R = ( \frac{7}{3}, \frac{3}{2} )$, $S = ( \frac{18}{7}, \frac{7}{7} )$. Which of the following statements is correct?

Let $\mathbf{| \mathbf{a} |} = 5$ and $-2 \leq z \leq 1$. Then, the range of $|\mathbf{a}|$ is:

For a Linear Programming Problem (LPP), the given objective function \( Z = 3x + 2y \) is subject to constraints: \[ x + 2y \leq 10, \] \[ 3x + y \leq 15, \] \[ x, y \geq 0. \]

The correct feasible region is:

Assertion (A): The shaded portion of the graph represents the feasible region for the given Linear Programming Problem (LPP).
Reason (R): The region representing \( Z = 50x + 70y \) such that \( Z < 380 \) does not have any point common with the feasible region.

A factory produces two products X and Y. The profit earned by selling X and Y is represented by the objective function \( Z = 5x + 7y \), where \( x \) and \( y \) are the number of units of X and Y respectively sold. Which of the following statements is correct?
Assertion (A): Every point of the feasible region of a Linear Programming Problem is an optimal solution.
Reason (R): The optimal solution for a Linear Programming Problem exists only at one or more corner point(s) of the feasible region.
In a Linear Programming Program (LPP) for objective function \( Z = 14x - 10y \) subject to the constraints: \[ x + y \leq 8, \quad 3x - 2y \geq -6, \quad x, y \geq 0 \] shade the feasible region and mark the corner points in a neatly drawn graph.
In the Linear Programming Problem for objective function \( Z = 18x + 10y \) subject to constraints \[ 4x + y \geq 20 \] \[ 2x + 3y \geq 30 \] \[ x, y \geq 0 \] Find the minimum value of \( Z \).

In the Linear Programming Problem (LPP), find the point/points giving the maximum value for \( Z = 5x + 10y\) subject to the constraints:
\[x + 2y \leq 120 \\ x + y \geq 60 \\ x - 2y \geq 0 \\ x \geq 0, y \geq 0\]

Solve the following linear programming problem graphically: \[ {Maximise } z = 4x + 3y, \quad {subject to the constraints:} \] \[ x + y \leq 800, \quad 2x + y \leq 1000, \quad x \leq 400, \quad x, y \geq 0. \]

Solve the following linear programming problem graphically: 
Maximize \( z = x + y \), subject to constraints: 
\[ 2x + 5y \leq 100, \quad 8x + 5y \leq 200, \quad x \geq 0, \quad y \geq 0. \]

The restrictions imposed on decision variables involved in an objective function of a linear programming problem are called:
It is given that function \( f(x) = x^4 - 62x^2 + ax + 9 \) attains a local maximum value at \( x = 1 \). Find the value of \( a \), hence obtain all other points where the given function \( f(x) \) attains local maximum or local minimum values.
A function \( f(x) = |1 - x + |x|| \) is:
The restrictions imposed on decision variables involved in an objective function of a linear programming problem are called: