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 2, 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) $
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The Correct Option isD
Solution and Explanation
Construct the following table of values of objective function:
Since the minimum value $(F) = 12$ occurs at two distinct corner points, it occurs at every point of the segment joining these two points.
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.
