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Questions › DSE › DSE 2009 › Q4
1 markMathematics › Constrained optimisation and linear programming › Equality-constrained optimisation and Lagrange multipliersModerateabout 2 min

DSE 2009 Question 4: Constrained optimisation and linear programming

Consider maximizing f(x,y)=x2−y2f(x,y)=x^{2}-y^{2}f(x,y)=x2−y2 subject to the constraint x+y=1x+y=1x+y=1, where xxx and yyy are real numbers. This problem has

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Consider maximizing f(x,y)=x²-y² subject to the constraint x+y=1, where x and y are real numbers. This problem has (A) no solution. (B) a unique solution. (C) 2 solutions. (D) an infinity of solutions.

Also written as: Consider maximizing f(x,y)=x^2-y^2 subject to the constraint x+y=1, where x and y are real numbers. This problem has

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.

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