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(a) Using the Lagrange multiplier method, find the values of a > 0 and b>0 that maximise the following function: h(a, b) = ln(a) + 3 ln(b) subject to the constraint: 5a + 2b = 40. Also include the value of the Lagrange multiplier, A. How do we know this is a global maximum for this constrained optimisation problem?

(a) Using the Lagrange multiplier method, find the values of a > 0 and b>0 that maximise the following function: h(a, b) = ln(a) + 3 ln(b) subject to the constraint: 5a + 2b = 40. Also include the value of the Lagrange multiplier, A. How do we know this is a global maximum for this constrained optimisation problem?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Using the Lagrange multiplier method, find the values of a > 0 and 6 > 0 that maximise the following function: h(a, b) = ln(a) + 3 ln (b) subject to the constraint: 5a + 2b = 40. Also include the value of the Lagrange multiplier, A. How do we know this is a global maximum for this constrained optimisation problem?
Transcribed Image Text:(a) Using the Lagrange multiplier method, find the values of a > 0 and 6 > 0 that maximise the following function: h(a, b) = ln(a) + 3 ln (b) subject to the constraint: 5a + 2b = 40. Also include the value of the Lagrange multiplier, A. How do we know this is a global maximum for this constrained optimisation problem?
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