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In the following problem, what is f (the function to optimize) and what is g (the restriction) ? Problem The plane 3x – 2y + z = 2 intersects the cylinder x + y? = 9 into some ellipse. Find the points on that ellipse the farthest from the origin. O function is f (æ, y) = x² + y? = 9 and restriction is g(x, y, z) = 3x – 2y + z = 2 O function is f (æ,y) = 3x – 2y + z = 2 and restriction is g(x, y, z) = x² + y² = 9 O function is f (x, y, z) = Væ² + y² + z² and restriction is g(x, y, z) = x² + y² = 9 O function is f (r, y, z) = /x² + y² + z² and restriction is g(x, y, z) = 3x – 2y + z O function is f (x, y, z) = Væ² + y² + z² Restriction 1: g1 (x, y, z) = 3x – 2y + z = 2 and Restriction 2: g2 (x, y, z) = x² + y² = 9 O There are two functions f(x, Y, z) = 3x² – 7z – xy = 0 and f(x,y) = x² + y² and there is one restriction "point should be the farthest from (0,0,0)."

In the following problem, what is f (the function to optimize) and what is g (the restriction) ? Problem The plane 3x – 2y + z = 2 intersects the cylinder x + y? = 9 into some ellipse. Find the points on that ellipse the farthest from the origin. O function is f (æ, y) = x² + y? = 9 and restriction is g(x, y, z) = 3x – 2y + z = 2 O function is f (æ,y) = 3x – 2y + z = 2 and restriction is g(x, y, z) = x² + y² = 9 O function is f (x, y, z) = Væ² + y² + z² and restriction is g(x, y, z) = x² + y² = 9 O function is f (r, y, z) = /x² + y² + z² and restriction is g(x, y, z) = 3x – 2y + z O function is f (x, y, z) = Væ² + y² + z² Restriction 1: g1 (x, y, z) = 3x – 2y + z = 2 and Restriction 2: g2 (x, y, z) = x² + y² = 9 O There are two functions f(x, Y, z) = 3x² – 7z – xy = 0 and f(x,y) = x² + y² and there is one restriction "point should be the farthest from (0,0,0)."

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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In the following problem, what is \( f \) (the function to optimize) and what is \( g \) (the restriction)? **Problem:** The plane \( 3x - 2y + z = 2 \) intersects the cylinder \( x^2 + y^2 = 9 \) into some ellipse. Find the points on that ellipse the farthest from the origin. 1. \( \quad \) Function is \( f(x, y, z) = x^2 + y^2 = 9 \) and restriction is \( g(x, y, z) = 3x - 2y + z = 2 \) 2. \( \quad \) Function is \( f(x, y, z) = 3x - 2y + z = 2 \) and restriction is \( g(x, y, z) = x^2 + y^2 = 9 \) 3. \( \quad \) Function is \( f(x, y, z) = \sqrt{x^2 + y^2 + z^2} \) and restriction is \( g(x, y, z) = x^2 + y^2 = 9 \) 4. \( \quad \) Function is \( f(x, y, z) = \sqrt{x^2 + y^2 + z^2} \) and restriction is \( g(x, y, z) = 3x - 2y + z \) 5. \( \quad \) Function is \( f(x, y, z) = \sqrt{x^2 + y^2 + z^2} \) Restriction 1: \( g_1(x, y, z) = 3x - 2y + z = 2 \) Restriction 2: \( g_2(x, y, z) = x^2 + y^2 = 9 \) 6. \( \quad \) There are two functions \( f(x, y, z) = 3x^2 - 7xz - xy = 0 \) and \( f(x, y) = x^2 + y^2 \) and there is one restriction "point should be the farthest from \((0,0,0)\)." The selected answer is option 4: Function is \( f(x, y, z) =
Transcribed Image Text:In the following problem, what is \( f \) (the function to optimize) and what is \( g \) (the restriction)? **Problem:** The plane \( 3x - 2y + z = 2 \) intersects the cylinder \( x^2 + y^2 = 9 \) into some ellipse. Find the points on that ellipse the farthest from the origin. 1. \( \quad \) Function is \( f(x, y, z) = x^2 + y^2 = 9 \) and restriction is \( g(x, y, z) = 3x - 2y + z = 2 \) 2. \( \quad \) Function is \( f(x, y, z) = 3x - 2y + z = 2 \) and restriction is \( g(x, y, z) = x^2 + y^2 = 9 \) 3. \( \quad \) Function is \( f(x, y, z) = \sqrt{x^2 + y^2 + z^2} \) and restriction is \( g(x, y, z) = x^2 + y^2 = 9 \) 4. \( \quad \) Function is \( f(x, y, z) = \sqrt{x^2 + y^2 + z^2} \) and restriction is \( g(x, y, z) = 3x - 2y + z \) 5. \( \quad \) Function is \( f(x, y, z) = \sqrt{x^2 + y^2 + z^2} \) Restriction 1: \( g_1(x, y, z) = 3x - 2y + z = 2 \) Restriction 2: \( g_2(x, y, z) = x^2 + y^2 = 9 \) 6. \( \quad \) There are two functions \( f(x, y, z) = 3x^2 - 7xz - xy = 0 \) and \( f(x, y) = x^2 + y^2 \) and there is one restriction "point should be the farthest from \((0,0,0)\)." The selected answer is option 4: Function is \( f(x, y, z) =
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