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Q3. Find the minimum of the function f(r, y) = r - y subject to the constraint r+ y? <1 Check the second order condition.

Q3. Find the minimum of the function f(r, y) = r - y subject to the constraint r+ y? <1 Check the second order condition.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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Q3. Find the minimum of the function f(r, y) = T - y subject to the constraint r + y? <1 Check the second order condition. Q4. Consider the problem of maximizing f(r, y) = r² - y subject to the constraint r2 + y <a, a > 0. 1. Set up Lagrangian, then write down the first order conditions and solve them. 2. Assume a <. Use the second order conditions to show that the point is a maximum of f. 3. Let a = . The solution in this case is (r, y) = (0, and A = 2/2. Use the envelope theorem to estimate the maximum of f subject to to r + 1.1y? <.
Transcribed Image Text:Q3. Find the minimum of the function f(r, y) = T - y subject to the constraint r + y? <1 Check the second order condition. Q4. Consider the problem of maximizing f(r, y) = r² - y subject to the constraint r2 + y <a, a > 0. 1. Set up Lagrangian, then write down the first order conditions and solve them. 2. Assume a <. Use the second order conditions to show that the point is a maximum of f. 3. Let a = . The solution in this case is (r, y) = (0, and A = 2/2. Use the envelope theorem to estimate the maximum of f subject to to r + 1.1y? <.
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