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en function G(x, y) = 3x² + + xy subject to the ofd I -24 constraint 2=2x+4y

en function G(x, y) = 3x² + + xy subject to the ofd I -24 constraint 2=2x+4y

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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Given function subject to the G (x, y) = 3 x ² + + xy - 2y ² - 2x + 4y - 1 constraint дех,у) = 8х+5у -24=0, Hence, the Lagrange function is I (x, y, x) = G(x,y) + x g(x, y) so, we olo o 2x ду are ƏL Эх = 3x²³+ / xy . zy² + 2x pay-1 ху-чуч + x (8x + 5y-24) = 6x + 1/7 y − 2 +81 - J.L ay g(x,y) (1 = =0 to 4 120 x - 4y + 4 + 57. solve these equations =0 -(¹1) or, 6x + 4y - 2+8X 20 4*- 4y +4 +5 × =0 (2) - (3). 8x4 57 - 24 = 0
Transcribed Image Text:Given function subject to the G (x, y) = 3 x ² + + xy - 2y ² - 2x + 4y - 1 constraint дех,у) = 8х+5у -24=0, Hence, the Lagrange function is I (x, y, x) = G(x,y) + x g(x, y) so, we olo o 2x ду are ƏL Эх = 3x²³+ / xy . zy² + 2x pay-1 ху-чуч + x (8x + 5y-24) = 6x + 1/7 y − 2 +81 - J.L ay g(x,y) (1 = =0 to 4 120 x - 4y + 4 + 57. solve these equations =0 -(¹1) or, 6x + 4y - 2+8X 20 4*- 4y +4 +5 × =0 (2) - (3). 8x4 57 - 24 = 0
froom (1) f (2), we get 6 x + 1²/22 y = 8 24x +y - 8 8 77 120x + 5 Now, 5y - 40 112x + 1 -2 +133y solving 14 x = If we then of G. 4x - 4y +4 5 40 = 27 is Therefore, Nalue of G at and there is 2-164 5 8x - 128y + =168 (3) 4 (4), y = Now, G₁ (¹ - 8/3) = 27. we want to know if 27 is the maximum oro minimum value. 8 no +16 - 3 PJ we get take the point G(3,0) = 27 +0 -0-6-1 <27. +128 (x,y) = (3,0) the maximum the point (^4 - 8/3) minimum valce
Transcribed Image Text:froom (1) f (2), we get 6 x + 1²/22 y = 8 24x +y - 8 8 77 120x + 5 Now, 5y - 40 112x + 1 -2 +133y solving 14 x = If we then of G. 4x - 4y +4 5 40 = 27 is Therefore, Nalue of G at and there is 2-164 5 8x - 128y + =168 (3) 4 (4), y = Now, G₁ (¹ - 8/3) = 27. we want to know if 27 is the maximum oro minimum value. 8 no +16 - 3 PJ we get take the point G(3,0) = 27 +0 -0-6-1 <27. +128 (x,y) = (3,0) the maximum the point (^4 - 8/3) minimum valce
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