Question:
The objective function $z = 4x_1 + 5x_2$, subject to $2x_1 + x_2 \geq 7 , 2x_1 + 3x_2 \leq 15 , x_2 \leq 3, x_1 , x_2 \geq 0 $ has minimum value at the point
The objective function $z = 4x_1 + 5x_2$, subject to $2x_1 + x_2 \geq 7 , 2x_1 + 3x_2 \leq 15 , x_2 \leq 3, x_1 , x_2 \geq 0 $ has minimum value at the point
Updated On: May 4, 2024
- On $x-axis$
- On $y-axis$
- At the origin
- On the line parallel to $x$-axis
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The Correct Option is A
Solution and Explanation
Answer (a) On $x-axis$
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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.