Question: The degree of an objective function of a linear programming problem is
Step 1 (Definition of Objective Function): [0.5 Mark]
In a Linear Programming Problem (LPP), the objective function is a linear function of the decision variables, typically represented as:
$$Z = ax + by$$where $a$ and $b$ are constants, and $x$ and $y$ are the decision variables. By definition, a "linear" function implies that the variables are raised to the power of 1.
Step 2 (Mathematical Analysis of Degree): [0.25 Mark]
The degree of a polynomial is defined as the highest power of the variable(s) present in the expression. In the expression $Z = ax^1 + by^1$, the highest exponent of the variables $x$ and $y$ is $1$.
Step 3 (Final Concluded Answer): [0.25 Mark]
Since the function must be linear to satisfy the constraints of an LPP, the degree must be $1$.
Correct Option: (B) 1
💡 EL10 Concept Insight: Think of a "linear" function like a straight line on a graph; because it doesn't curve or bend, the variables inside it can only have a power of 1, which is why the degree is always 1.