Consider the problem of maximizing with respect to subject to the constraint , where is a parameter taking some fixed value greater than . Let be the value attained, as a function of , and let be its derivative. Which of the following is correct?
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Consider the problem of maximizing f(x,y) = x² + 2xy + by² with respect to x, y subject to the constraint x + y = 100, where b is a parameter taking some fixed value greater than 1. Let v(b) be the value attained, as a function of b, and let v′(b) be its derivative. Which of the following is correct? (A) v′(b) > 0 (B) v′(b) < 0 (C) v′(b) = 0 (D) The sign of v′(b) changes with b
Also written as: Consider the problem of maximizing f(x,y) = x^2 + 2xy + by^2 with respect to x, y subject to the constraint x + y = 100, where b is a parameter taking some fixed value greater than 1. Let v(b) be the value attained, as a function of b, and let v'(b) be its derivative. Which of the following is correct?
Constrained optimisation and linear programming has come up 44 times in 7 exams since 2007.
This question is on Inequality constraints, second-order conditions and envelope theorem, part of Constrained optimisation and linear programming in Mathematics.
Optima with inequality constraints, tests for maxima, and how the optimal value changes with parameters.
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Question from the DSE 2021 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.