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example, utility maximizing individuals are constrained by a budget constraint.) There are two widely used methods for solving constrained optimization problems. I. The Substitution Method A. The Substitution Method. In some cases, it is possible to "substitute" the constraint into the objective function (the function being maximized) to create ... 3 Substitution method The substitution method for solving recurrences has two parts. 1. Guess the correct answer. 2. Prove by induction that your guess is correct. 4 Example Use the substitution method to solve T(n) = 2T(n/2)+n. Guess: T(n) = O(nlgn) Proof: Use induction on n to show that there exist c and n 0 for which T(n) ≤ cnlgn for all n ...

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