Find the unique critical point of f(x, y, z) = 40x + 30y − z(20xy – 10) that has all positive entries. Hint: Solve the equations fx = 0 and fy = 0 for z, use the results to express y in terms of x (or vice versa), and then continue on to the equation f₂ = 0. © ... (x*, y*, z*) = (√5/3, √6, √8/3) O · (x*, y*, z*) = (√/3/8, √2/3, √√6) ... ○... (x, y, z) = (√6/5, √5/3, √6) · (x*, y*, z*) = (√/4/3√ √/2/3,√7) O

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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Question
Find the unique critical point of f(x, y, z) = 40x + 30y − z(20xy – 10) that has all positive
entries.
Hint: Solve the equations fx = 0 and fy = 0 for z, use the results to express y in terms of x (or
vice versa), and then continue on to the equation f₂ = 0.
© ... (x*, y*, z*) = (√5/3, √6, √8/3)
O · (x*, y*, z*) = (√/3/8, √2/3, √√6)
...
○... (x, y, z) = (√6/5, √5/3, √6)
· (x*, y*, z*) = (√/4/3√ √/2/3,√7)
O
Transcribed Image Text:Find the unique critical point of f(x, y, z) = 40x + 30y − z(20xy – 10) that has all positive entries. Hint: Solve the equations fx = 0 and fy = 0 for z, use the results to express y in terms of x (or vice versa), and then continue on to the equation f₂ = 0. © ... (x*, y*, z*) = (√5/3, √6, √8/3) O · (x*, y*, z*) = (√/3/8, √2/3, √√6) ... ○... (x, y, z) = (√6/5, √5/3, √6) · (x*, y*, z*) = (√/4/3√ √/2/3,√7) O
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