The degree of an objective function of a linear programming problem is

Q: The degree of an objective function of a linear programming problem is

The correct option is **(B) 1**. **Reasoning:** An objective function in a linear programming problem is always a *linear* function of the decision variables (of the form $Z = ax + by$), and a linear expression has degree 1 by definition.

Q: Does the number of variables in the objective function change its degree?

No. Whether the objective function has 2 variables ($Z = ax + by$) or 10 variables, every term remains degree 1 as long as it is linear, so the overall degree stays 1.

Linear Programming

Linear Programming - Objective Function

Options

(A)0

(B)1

(D)Any natural number

Official Answer

The correct option is (B) 1.

Reasoning: An objective function in a linear programming problem is always a linear function of the decision variables (of the form $Z = ax + by$ ), and a linear expression has degree 1 by definition.

linear programmingobjective functiondegree of a functionlinear functiondecision variablesLPP formulation

Marking Scheme

11 mark: correct option (B) 1 — no partial marking for MCQ.

Hint

Recall that 'linear' in Linear Programming means the objective function is always degree 1.

Quick Oral Answer

The objective function in any LPP is linear by definition — $Z = ax + by$ — so its degree is always 1.

Analysis & Explanation

Why (B) is correct: By definition, an LPP objective function is a linear function of the decision variables, $Z = ax + by$ (in two variables) or $Z = a_1x_1 + a_2x_2 + \ldots + a_nx_n$ in general — every term has power 1, so its degree is always 1, regardless of the number of variables.

Why the distractors are wrong:

(A) 0 would mean Z is a constant, which cannot represent a meaningful optimization objective.
(C) 2 would mean the function is quadratic (e.g., involves $x^2, xy, y^2$ ), which is outside the scope of linear programming by definition.
(D) 'Any natural number' confuses LPP with general (nonlinear) optimization — the word 'linear' in LPP specifically restricts the objective function's degree to exactly 1.

Common Mistakes

1Assuming the degree can vary with the number of variables in the objective function.
2Confusing 'linear programming' with general optimization, where the objective function could be nonlinear.

Interesting Facts

The word 'programming' in Linear Programming has nothing to do with computer coding — it was coined in the 1940s to mean 'planning' or 'scheduling' of resources.

Even though the objective function is always degree 1 (linear), the feasible region it is optimized over can be defined by any number of linear inequality constraints, forming a convex polygon (in 2D) or polytope (in higher dimensions).

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Frequently Asked Questions

Why is the objective function of an LPP always linear?

Because Linear Programming is specifically defined to deal with optimization problems where both the objective function and the constraints are linear (degree-1) expressions in the decision variables — this restriction is what makes graphical and simplex methods applicable.

Does the number of variables in the objective function change its degree?

No. Whether the objective function has 2 variables ( $Z = ax + by$ ) or 10 variables, every term remains degree 1 as long as it is linear, so the overall degree stays 1.