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Questions › IIT JAM › IIT JAM 2023 › Q60
2 marksMathematics › Constrained optimisation and linear programming › Equality-constrained optimisation and Lagrange multipliersHardabout 3 min

IIT JAM 2023 Question 60: Constrained optimisation and linear programming

If (x∗,y∗)(x^*,y^*)(x∗,y∗) solves: maximise f(x,y)=100−e−x−e−yf(x,y)=100-e^{-x}-e^{-y}f(x,y)=100−e−x−e−y subject to ex+y=ee−1ex+y=\tfrac{e}{e-1}ex+y=e−1e​, x≥0x\ge0x≥0, y≥0y\ge0y≥0, then y∗x∗\sqrt{\tfrac{y^*}{x^*}}x∗y∗​​ is ________ (round off to 2 decimal places).

Answer and worked solution

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Plain-text version

If (x*,y*) solves: maximise f(x,y)=100-e^(-x)-e^(-y) subject to ex+y=e/(e-1), x≥0, y≥0, then √(y*/x*) is (round off to 2 decimal places).

Also written as: If (x*,y*) solves: maximise f(x,y)=100-e^(-x)-e^(-y) subject to ex+y=e/(e-1), x>=0, y>=0, then sqrt(y*/x*) is (round off to 2 decimal places).

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

What this question tests

This question is on Equality-constrained optimisation and Lagrange multipliers, part of Constrained optimisation and linear programming in Mathematics.

Optimising a function subject to equality constraints, and what the multiplier means.

TestStop has 14 past-paper questions on this subtopic.

Take this paper as a timed mockMore on Equality-constrained optimisation and Lagrange multipliers

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Question from the IIT JAM 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.