The optimal value of the objective function is obtained at the points
The optimal value in linear programming refers to the best possible solution for the objective function, whether it’s maximization or minimization. It is found at the vertices of the feasible region defined by the constraints. The optimal value ensures the best outcome under given limitations or requirements.
Linear Programming in Chapter 12 of Class 12 Maths involves optimizing a linear objective function subject to linear constraints. It aims to find the best possible solution within the feasible region formed by these constraints. The optimal solution lies at one of the vertices of this feasible region, widely used in economics and business for decision-making.
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The optimal value of the objective function in LPP is always obtained at the corner points of the feasible region.
This is because the objective function is linear, and at one of the corner points due to the property of linear programming, the maximum or minimum occurs.
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https://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-12