AMU 2026 — Mathematics PYQ

Linear Programming is based on a set of fundamental assumptions that ensure the model can be solved using deterministic mathematical methods. The core assumptions include:

1. Proportionality: The contribution of each decision variable to the objective function and its consumption of resources is directly proportional to its value. If you double the amount of a product, you double the profit and the resource usage.

2. Additivity: The total contribution to the objective function and the total resource usage is the sum of the individual contributions/usages of each variable. There are no interactions between variables.

   • Mathematically: $f(x_1+x_2)=f(x_1)+f(x_2)$

3. Divisibility: Variables are assumed to be continuous, meaning they can take on non-integer (fractional) values.

4. Certainty: All parameters (coefficients in constraints and the objective function) are assumed to be known constants. There is no randomness or uncertainty involved in the input data.

Note: Because LPP assumes that all parameters are perfectly known and fixed, "Uncertainty" is the factor that does not belong to the standard LPP framework. If uncertainty were present, the model would move into the realm of Stochastic Programming or Fuzzy Linear Programming.