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In a LPP, what is the linear function Z=...

In a LPP, what is the linear function Z=ax+by called?

A

Profit function

B

Loss function

C

Objective function

D

None of these

Text Solution

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The correct Answer is:
To solve the question, we need to identify what the linear function \( Z = ax + by \) is referred to in the context of linear programming problems (LPP). ### Step-by-Step Solution: 1. **Understanding Linear Programming**: Linear programming is a method used to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. 2. **Identifying the Function**: In the given function \( Z = ax + by \), \( Z \) represents a value that we want to either maximize or minimize. The variables \( x \) and \( y \) are subject to certain constraints. 3. **Objective of Linear Programming**: The main goal in linear programming is to find the maximum or minimum value of the objective function, which is typically represented as \( Z \). 4. **Definition of the Objective Function**: The function \( Z = ax + by \) is specifically called the **objective function** in linear programming. This is because it defines the objective of the problem, which is to maximize or minimize the value of \( Z \) based on the constraints provided. 5. **Conclusion**: Therefore, in the context of the question, the linear function \( Z = ax + by \) is referred to as the **objective function**. ### Final Answer: The linear function \( Z = ax + by \) is called the **objective function** in a linear programming problem.
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