Question:
Fill in the blanks
$ (i)$ In a $LPP$, the objective function is always
$(ii)$ The feasible region for a $LPP$ is always a polygon.
$(iii)$ A feasible region of a system of linear inequalities is said to be , if it can be enclosed within a circle.
$(iv)$ In a $LPP$, if the objective function $Z = ax + by$
has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same value.
Fill in the blanks
$ (i)$ In a $LPP$, the objective function is always
$(ii)$ The feasible region for a $LPP$ is always a polygon.
$(iii)$ A feasible region of a system of linear inequalities is said to be , if it can be enclosed within a circle.
$(iv)$ In a $LPP$, if the objective function $Z = ax + by$
has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same value.
Updated On: Jul 6, 2022
- a
- b
- c
- d
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The Correct Option is D
Solution and Explanation
$(i)$ In a $LPP$, objective function is always linear.
$(ii)$ The feasible region for a $LPP$ is always a convex polygon.
$(iii)$ A feasible region of a system of linear inequalities is said to be bounded, if it can be enclosed within a circle.
$ (iv)$ In a $LPP$, if the objective function $Z = ax + by$ has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same maximum value.
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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.