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A linear function, which is minimized or...

A linear function, which is minimized or maximized is called an optimal point.

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To determine whether the statement "A linear function, which is minimized or maximized is called an optimal point" is true or false, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Terms**: - A **linear function** is a function of the form \( z = ax + by + c \), where \( a \), \( b \), and \( c \) are constants. - An **objective function** is the function that we aim to maximize or minimize in a linear programming problem. 2. **Identifying the Statement**: - The statement claims that a linear function that is minimized or maximized is called an "optimal point." 3. **Clarifying the Concept of Optimal Point**: - An **optimal point** refers to the specific values of the variables (such as \( x \) and \( y \)) that yield the maximum or minimum value of the objective function. - It is not the function itself that is called the optimal point, but rather the point (or points) at which the maximum or minimum occurs. 4. **Conclusion**: - Since the statement incorrectly identifies a linear function as an optimal point, the statement is **false**. The correct terminology is that the maximum or minimum value of the objective function occurs at the optimal point, not that the function itself is called an optimal point. ### Final Answer: The statement is **false**. ---
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