Question:

Inequations $3x - y \geq 3 $ and $4x - y \geq 4 $

Updated On: Jul 6, 2022
  • Have solution for positive x and y
  • Have no solution for positive x and y
  • Have solution for all x
  • Have solution for all y
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The Correct Option is A

Solution and Explanation

Following figure will be obtained on drawing the graphs of given inequations. From $3x - y \geq 3, \frac{x}{1} + \frac{y}{-3} = 1 $ From $4x - y > 4, \frac{x}{1} + \frac{y}{-4} = 1$ Clearly the common region of both is true for positive value of (x, y). It is also true for positive value of x and negative value of y.
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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.