AMU 2026 — Mathematics PYQ

1. What are Decision Variables?

In a Linear Programming Problem (LPP), decision variables are the unknown quantities that the model aims to determine (e.g., the number of units of product $A$ to produce, or the amount of resources to allocate). These variables are typically denoted as $x_1,x_2,\dots ,x_n$ or $x,y,z$.

2. The Non-Negativity Constraint

Linear programming models operate under the foundational assumption that the quantities represented by the decision variables cannot be negative. This is because, in most real-world applications (like manufacturing, finance, or logistics), producing a negative number of items or allocating negative resources is physically impossible or meaningless.

To represent this mathematically, we include a non-negativity constraint:

$$x_j\ge 0\text{for all }j=1,2,\dots ,n$$

This ensures that the solution space remains within the first quadrant (in 2D) or the positive orthant (in higher dimensions), making the variables non-negative.

Conclusion

While decision variables can be zero, they must be greater than or equal to zero to be physically valid in an LPP framework. Thus, they are classified as non-negative.

This directly matches option (c).