Non-negative condition in an LP model implies Select one:
a. Non-negative value of resourse
b. A positive coefficient of variables in objective function
c. No restrictions
d. A positive coefficient of variables in any constraint .
The correct answer and explanation is:
Correct Answer: a. Non-negative value of resource
Explanation:
In a Linear Programming (LP) model, the non-negativity constraint ensures that decision variables cannot take negative values. This is essential in real-world optimization problems where negative values would be unrealistic, such as in resource allocation, production levels, or transportation problems.
Why Non-Negativity is Important?
- Practical Relevance: Many LP models deal with quantities like labor hours, raw materials, money, or goods, which cannot be negative.
- Mathematical Feasibility: The simplex method and other optimization algorithms rely on non-negative values to compute feasible solutions.
- Logical Consistency: If decision variables were allowed to be negative, it could lead to absurd results—such as producing negative units of a product, which is meaningless.
How It Affects an LP Model?
- Constraints: Non-negativity affects constraints by ensuring that resources are either utilized or left unused, but never consumed in negative amounts.
- Objective Function: While non-negativity does not directly impact whether coefficients in the objective function are positive or negative, it ensures that the optimization process works within practical limits.
- Feasible Region: The non-negative restriction defines a feasible solution space where only realistic solutions exist.
Thus, the correct choice is (a) Non-negative value of resource, as non-negativity constraints ensure all resources and variables remain at realistic, non-negative values.
Now, I’ll generate an image representing a basic LP model with a feasible region, illustrating the impact of non-negativity constraints.
Here is the graphical representation of a Linear Programming (LP) model with a feasible region constrained by non-negativity conditions. Let me know if you need any modifications!
