Question:

The maximum value of $z = 3x + 4y$ subject to the condition $x + y \le 40, x + 2y \le 60, x,y \ge 0$ is

Updated On: Jul 5, 2022

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The Correct Option is D

Solution and Explanation

Obviously, $z = 3x + 4y$ will be maximum at $(20,\, 20)$ $\therefore$ Max $z = 3 ? 20 + 4 ? 20 = 60 + 80 = 140$

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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.