Question:
The feasible region of an LPP is shown in the figure . If $z = 3x + 9y ,$ then the minimum value of z occurs at
The feasible region of an LPP is shown in the figure . If $z = 3x + 9y ,$ then the minimum value of z occurs at
Updated On: May 17, 2024
- (5,5)
- (0,10)
- (0,20)
- (15,15)
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The Correct Option is A
Solution and Explanation
Corner Points
z = 3x + 9y
(5, 5)
z = 60
(0, 10)
z = 90
(0, 20)
z = 180
(15, 15)
z = 180
$\therefore$ Minimum value of z occurs at (5, 5)
z = 3x + 9y
(5, 5)
z = 60
(0, 10)
z = 90
(0, 20)
z = 180
(15, 15)
z = 180
$\therefore$ Minimum value of z occurs at (5, 5)
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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.