The objective function of an LPP is A) a constraint B)a function to be optimised C) a relation between the variables D) none of these

Options

A. a constraint
B. a function to be optimised
C. a relation between the variables
D. None of the above

Explanation

To solve the question regarding the objective function of a Linear Programming Problem (LPP), we can break it down step by step.

### Step-by-Step Solution:

1. **Understanding LPP**:
A Linear Programming Problem (LPP) involves optimizing a linear objective function, subject to a set of linear inequalities or equations known as constraints.

**Hint**: Remember that LPP is used to find the best outcome in a mathematical model whose requirements are represented by linear relationships.

2. **Objective Function**:
The objective function in an LPP is the function that we want to maximize or minimize. It is typically expressed in the form:
\[ Z = c_1x_1 + c_2x_2 + ... + c_nx_n \]
where \(Z\) is the objective function, \(c_1, c_2, ..., c_n\) are the coefficients, and \(x_1, x_2, ..., x_n\) are the decision variables.

**Hint**: Identify the coefficients and variables in the objective function; they represent the quantities you are trying to optimize.

3. **Maximization and Minimization**:
Depending on the problem, the objective function can either be maximized (e.g., profit) or minimized (e.g., cost). The goal is to find the optimal values of the decision variables that yield the best value of the objective function.

**Hint**: Determine whether the context of the problem requires you to maximize or minimize the objective function.

4. **Conclusion**:
Therefore, the objective function of an LPP is the function that is to be optimized (either maximized or minimized) based on the constraints provided.

**Hint**: Always check the constraints as they will guide you in finding the feasible region for the optimization.

### Final Answer:
The objective function of an LPP is the function that is to be optimized (maximized or minimized) based on the constraints of the problem.