Consider
Minimize $z = 3x + 2y$
subject to $x + y \geq 8 $
$3x + 5y \leq 15$
$x, y \geq 0$
It has :
- Infinite feasible solutions
- Unique feasible solution
- No feasible solution
- None of these
The Correct Option is C
Solution and Explanation
Top Questions on Linear Programming Problem
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.
- CBSE CLASS XII - 2025
- Mathematics
- Linear Programming Problem
- 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 $Z$.
- CBSE CLASS XII - 2025
- Mathematics
- Linear Programming Problem
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.- CBSE CLASS XII - 2025
- Mathematics
- Linear Programming Problem
- Let $\mathbf{| \mathbf{a} |} = 5$ and $-2 \leq z \leq 1$. Then, the range of $|\mathbf{a}|$ is:
- CBSE CLASS XII - 2025
- Mathematics
- Linear Programming Problem
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.
- CBSE CLASS XII - 2025
- Mathematics
- Linear Programming Problem
Concepts Used:
Linear Programming
Linear programming is a mathematical technique for increasing the efficiency and effectiveness of operations under specific constraints. The main determination of linear programming is to optimize or minimize a numerical value. It is built of linear functions with linear equations or inequalities restricting variables.
Characteristics of Linear Programming:
- Decision Variables: This is the first step that will determine the output. It provides the final solution to the problem.
- Constraints: The mathematical form in which drawbacks are expressed, regarding the resource.
- Data: They are placeholders for known numbers to make writing complex models simple. They are constituted by upper-case letters.
- Objective Functions: Mathematically, the objective function should be quantitatively defined.
- Linearity: The function's relation between two or more variables must be straight. It indicates that the variable's degree is one.
- Finiteness: Input and output numbers must be finite and infinite. The best solution is not possible if the function consists infinite components.
- Non-negativity: The value of the variable should be either positive (+ve) or 0. It can't be a negative (-ve) number.