Question:

Corner points of the feasible region for an LPP are (0, 2) (3, 0) (6, 0), (6, 8) and (0, 5). Let F = 4x + 6y be the objective function. The minimum value of F occurs at

Updated On: Mar 19, 2024
  • (0, 2) only
  • (3, 0) only
  • the mid-point of the line segment joining the points (0, 2) and (3, 0) only
  • any point on the line segment joining the points (0, 2) and (3, 0)
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is D

Solution and Explanation

As seen here, at (0,2) and (3,0) points the obtained value of the equation 4x+6y = 12, which will minimum values among all.

The task of obtaining the most efficient optimal (maximum or lowest) value of a linear function with several variables (referred to as the objective function) is known as a linear programming problem (or LPP). Some requirements for LLP include that the variables fulfill a set of linear inequalities (also known as linear constraints) and be non-negative. These variables are non-negative and are also referred to as choice variables. Manufacturing issues, dietary issues, and transportation issues are the three main categories of linear programming problems.

The number of problems that can be optimized with linear programming has no upper bound. The most prevalent sorts of issues on board examinations are these three:

  1. Manufacturing Issues: In these issues, we maximize profit while utilizing the fewest resources possible.
  2. Diet Problem: To lower the cost of production, we compute the quantity of different nutrients in a diet.
  3. Transportation Problem: In these issues, we compute the timetable to identify the most expedient and affordable means of shipping a product.
Was this answer helpful?
1
0

Top Questions on Linear Programming Problem

View More Questions

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.