The functional constraints of a linear model with nonnegative variables are 3X₁ + 5X₂ $\le$ 16 and 4X₁ + X₂ $\le$10.Which of the following points could not be an optimal solution for the model? A)X₁ = 2.5, X₂= 0 B)X₁ = 0, X₂= 3.2 C)X₁ = 1, X₂= 2.25 D)X₁ = 2, X₂= 2

Question

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The constraints given are 3x + 5y ≤ 16 and 4x + y ≤ 10. Substituting the values from option C (x=1, y=2.25) into the constraints: For the first constraint, 3(1) + 5(2.25) = 3 + 11.25 = 14.25, which satisfies the first constraint. For the second constraint, 4(1) + 2.25 = 4 + 2.25 = 6.25, which also satisfies the second constraint. However, the question asks for a point that could not be an optimal solution, implying a misunderstanding in the interpretation of the constraints or the question's intent. Given the constraints and the options, all provided points actually satisfy the given linear inequalities, suggesting a potential error in the question's formulation or in the selection of the correct answer based on the provided information.

The Functional Constraints of a Linear Model with Nonnegative Variables ≤\le≤

The Functional Constraints of a Linear Model with Nonnegative Variables $\le$