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Questions › DSE › DSE 2009 › Q29
2 marksMathematics › Constrained optimisation and linear programming › Inequality constraints, second-order conditions and envelope theoremModerateabout 3 min

DSE 2009 Question 29: Constrained optimisation and linear programming

f(c)=max⁡2x+y=c, x≥0, y≥0(x+2y)f(c)=\max_{2x+y=c,\ x\ge 0,\ y\ge 0}(x+2y)f(c)=max2x+y=c, x≥0, y≥0​(x+2y). Find f′(c)f'(c)f′(c).

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f(c)=max_(2x+y=c, x≥ 0, y≥ 0)(x+2y). Find f′(c). (A) c (B) 0 (C) 2 (D) c/2

Also written as: f(c)=max_(2x+y=c, x>= 0, y>= 0)(x+2y). Find f'(c).

Constrained optimisation and linear programming has come up 44 times in 7 exams since 2007.

What this question tests

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.

TestStop has 8 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2021 · Q55The optimal value of: minimize 2xy subject to 9x² + 4y² ≤ 36 is _ (in integer).
Practise Constrained optimisation and linear programmingMore on Inequality constraints, second-order conditions and envelope theorem

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Question from the DSE 2009 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.