Question:
Consider
Minimize $z = 3x + 2y$
subject to $x + y \geq 8 $
$3x + 5y \leq 15$
$x, y \geq 0$
It has :
Consider
Minimize $z = 3x + 2y$
subject to $x + y \geq 8 $
$3x + 5y \leq 15$
$x, y \geq 0$
It has :
Updated On: Jul 6, 2022
- Infinite feasible solutions
- Unique feasible solution
- No feasible solution
- None of these
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The Correct Option is C
Solution and Explanation
Given problem is minimize z = 3x + 2y subject to x +y $\geq$ 8,
3x + 5y $\leq$ 15
x, y $\geq$ 0
First we convert these inequations into equations and draw the graph.
Since, there is no feasible region, therefore no feasible solution.
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Notes on 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.