Which of the following are assumptions of linear programming?
(A) Complexity
(B) Additivity
(C) Multiplicity
(D) Infiniteness
Choose the correct answer from the options given below:
(A) Complexity
(B) Additivity
(C) Multiplicity
(D) Infiniteness
Choose the correct answer from the options given below:
Show Hint
Proportionality
Additivity
Divisibility
Certainty
This helps you identify the correct assumptions.
- (A) and (C) only.
- (C) and (D) only.
- (B) only.
- (B) and (D) only.
The Correct Option is C
Solution and Explanation
Linear Programming (LP) is a mathematical optimization technique.
The validity of an LP model depends on several key assumptions: Proportionality, Additivity, Divisibility, Certainty, and Finiteness.
Detailed Explanation:
Let us evaluate each option against these core assumptions:
- (A) Complexity: Complexity describes real-world scenarios, but it is not a mathematical assumption of LP. LP models simplify complexity by assuming linear relationships. Thus, (A) is not an assumption.
- (B) Additivity: This is a core assumption, stating that the total output or resource use is equal to the sum of the outputs or resources used by each individual activity. Thus, (B) is a valid assumption.
- (C) Multiplicity: LP models assume single-valued coefficients (certainty) rather than multiple values. Thus, (C) is not an assumption.
- (D) Infiniteness: LP models assume finiteness (a finite number of decision variables and constraints) to remain solvable. Infiniteness would make the problem mathematically intractable. Thus, (D) is not an assumption.
Therefore, only (B) Additivity is a standard assumption of linear programming.
Step 2: Final Answer:
This matches Option (C).
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