Question

Which of the following is a key assumption in linear programming?

• A. The relationship between variables is nonlinear
• B. Variables can only take integer values
• C. The objective function and constraints are linear
• D. There are no constraints on variables

Hint:

The name "Linear Programming" itself highlights the main assumption of the method.
The relationships must be strictly linear, which means there are no product terms like $x_1 x_2$ or powers like $x_1^2$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the primary mathematical assumption that defines a Linear Programming (LP) model.

Step 2: Key Formula or Approach: This is a theoretical question. Linear programming is an optimization technique where both the objective function and the set of constraints must be represented by linear relationships of the decision variables.

Step 3: Detailed Explanation:

• The core assumption of Linear Programming is linearity, which consists of two properties: proportionality and additivity.

• Proportionality means the contribution of each decision variable to the objective function or constraints is directly proportional to the value of that variable.

• Additivity means the total contribution of all variables is the sum of their individual contributions.

• Together, these properties ensure that the objective function and constraints can be written as linear algebraic equations or inequalities.

• Standard LP allows continuous variables (violating Option B, which describes Integer Programming).

• Unconstrained problems (Option D) do not represent linear programming, as constraints are a fundamental part of the model.

Step 4: Final Answer:
The key assumption in linear programming is that the objective function and constraints are linear.