Find the minimum and maximum values of the function f(x, Y, z) = 3x + 2y+ 4z subject to the constraint r? + 2y² + 6z² = 1. fmaz = fmin

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Q: Find maximum and minumum values of f(x, y, z) = 2x – 4y + 10z subject to the constraint x² + y² + z²…

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Q: Find the maximum of f(x, y, z) = x + y + z subject to the two constraints x 2 + y2 + z2 = 9 and ¼x2…

A: Let’s define g(x, y, z) = x 2 + y2 + z2 - 9 and h(x, y, z) = ¼x2 + ¼Y2 + 4z2 - 9 So the problem is…

Q: Find the minimum and maximum of f(x, y, z) = x² + y² + z² subject to two constraints, x + 2y + z = 1…

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Q: Use the method of Lagrange multipliers to maximize the function subject to the given constraints.…

A: We have to use method of langrages Multipliers to find maximum and minimum values.

Q: · f(x, y, z) = x² + y² + z² subject to the constraint 0 = x² - y² + 1

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Q: f (x, y, z) = 2x² + 4y² + 5 where x² + y² – 2x + z = 0.

A: Here, the given function is: f(x,y,z)=2x2+4y2+5...(1) with the constraint…

Q: Find the minimum and maximum values of the function f(x,y,z)=3x+2y+4zf(x,y,z)=3x+2y+4z subject to…

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Q: The given function subject to the constraint 38−x−3y−z=0 has a minimum at x=___________,…

A: Let fx,y,z=x2+y2+z2-2x-2y-2z+3gx,y,z=x+3y+z=38∇fx,y,z=λ∇gx,y,zfx,fy,fz=λgx,gy,gzcompute partial…

Q: Maximize the function ƒ(x, y, z) = x2 + 2y - z2 subject to the constraints 2x - y = 0 and y + z = 0.

A: Given:  The function is  f(x,y,z)=x2+2y-z2And subject to the constraints  2x-y=0 and y+z=0

Q: 4. Use Lagrange multipliers to find the maximum and minimum values of the function subject to the…

A: To find the maximum and minimum values of the function f(x,y,z)=xyz subjected to the constraint…

Q: Find maximum and minumum values of f(x, y, z) = 2x – 4y + 10z subject to the constraint x2 +y? + z²…

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Q: Find the extreme values of f(x, y, z) = x + 2y + 3z subject to the two constraints x + y + z = 1 and…

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Q: Find maximum and minimum lues of f(x, y,z). 8X -16y+ 407 subject to %3D constraint x2+ y2+ 22 - 750

A: To find the maximum and minimum value of function

Q: Find the maximum value of f(1, y, z) = ry + Iz+ yz – 4ryz | subject to the constraints z+y+z=8 and…

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Q: Find the minimum and maximum values of the function f(x, y, z) = 3x + 2y + 4z subject to the…

A: Introduction: When we extremize a multi variable function under certain constraints, we follow the…

Q: Find maximum and minumum values of f(x, y, z) = 7x – 14y + 35z subject to the constraint x² + y? +…

A: Use Lagrange multipliers and find maximum, minimum value.

Q: Minimize the function ƒ(x, y, z) = x2 + y2 + z2 subject to the constraints x + 2y + 3z = 6 and x +…

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Q: Find maximum and minumum values of f(x, Y, z) = 2x – 4y + 10z subject to the constraint a? + y? + 22…

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Q: Find the maximum of f (x, y, z) = xyz subject to the constraintg(x, y, z) = 2x + y + 4z = 1.

A: Let us assume  fx,y,z=xyz and gx,y,z≡2x+y+4z−1=0Using lagrange multiplier…

Q: Find the maximum and minimum values of f(x, y, z) = xyz subject to the constraint x+y+z% 1. Assume…

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Q: Find maximum and minumum values of f(x, y, z) = 7x - 14y + 35z subject to the constraint x² + y? +…

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Q: Find the minimum and maximum values of the function f (x, y, z) 3x + 2y + 4z subject to the…

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Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint x? +y² + z²…

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Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint z? + y? +…

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Q: Find the maximum and minimum values of f(x, y, z) = x +y + z2 subject to the constraints x +y+z =1…

A: To find the maximum value of the function f(x,y,z), subject to the the constraints gx,y,z=0 and…

Q: Find the maximum and minimum values of the function f(x, y, z) = 3x – y – 3z subject to the…

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Q: Find the extreme values of the function subject to the given constraint. f(x, y, z) = (x - 1)2 +…

A: As per company guidelines we are allowed to solve one equation at a time so i am solving first one…

Q: Find the minimum value of f(x,y,z) = x 2 + y 2 + z2 subject to two constraints, x + 2y + z = 3 and x…

A: fx,y,z=x2+y2+z2 Lets solve using substitution method- x-y=4⇒x=4+y…

Q: Find the minimum of the function f(x, y) = x² + y² – xy subject to the constraint 2æ + 2y = 2. Value…

A: We have to find the minimum of the function fx,y=x2+y2-xy subject to the constraint 2x+2y=2.

Q: Find maximum and minumum values of f(x, y, z) = 2x – 4y + 10z subject to the constraint x? + y? + z2…

A: Z27272

Q: Find the maximum value of Z = 2x + 3y +y< 30, y 2 3, 0<ys 12, x – y 2 0, and 0<x < 20. subiect to…

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Q: Find maximum and minumum values of f(æ, y, 2) = 5¤ – 10y + 25z subject to the constraint a? + y? +…

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Q: 3. Let f(x, y) = xe" subject to the constraint x2 + y2 = 2. Find the minimum value and the maximum…

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Q: Find maximum and minumum values of f(x, Y, 2) = 3x – 6y + 15z subject to the constraint a? + y? + 2ª…

A: given, f(x,y,z)=3x-6y+15zsubject to constraint x2+y2+z2=1080

Q: Find the maximum off (x, y, z) = xyz subject to the constraint g(x, y, z) = 2x + y + 4z = l.

A: Let f(x,y,z) = xyz and g(x,y,z) = 2x + y + 4z - 1 The gradient vectors of f and g are given by: We…

Q: The maximum value M and the minimum value m of f(x,y)=x³-2y² subject to the constraint x3+y3=125 are…

A: Apply the Lagrange's multiplier method, ∂f∂x=λ∂g∂x⇒3x2=λ(3x2)⇒3x2(λ-1)=0⇒x=0 ; λ=1Also,…

Q: Minimize ƒ(x, y, z, w) = x2 + y2 + z2 + w2 subject to the constraints 2x - y + z - w - 1 = 0 and x +…

A: Use the Lagrange Multiplier technique with two constraints, to find the value of x,y,z,w at which…

Q: Find the maximum of the following function: h(x, y)  =  ln(x10 y6) given the constraints: 5x2 +…

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Q: Find the minimum and maxinum of f(x, y, 2) HỰ +2 subject to two constraints, z + 2y +z=8 and z- y =…

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Q: Find maximum and minumum values of f(x, y, z) = 5x – 10y + 25z subject to the constraint a2 +y² + z²…

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Q: Find maximum and minumum values of f(x, y, z) = 7x – 14y + 35z subject to the constraint 2 + y² + z²…

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Q: Find the maximum of V = xyz subject to the constraint 6x+4y+3z-24=0

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Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint a2 + y² +…

A: solution is given below

Q: Minimize f(x,y,z) = 3x2+4y2+6z2 subject to the constraint 3x+7y+8z=20. a.) When the minimum…

A: Given that , fx,y,z=3x2+4y2+6z2 and gx,y,z=3x+7y+8z-20 According to our guidelines , We can answer…

Q: Find the maximum value of the function f(r, y) = x²y subject to the constraint z² +y= 5. %3D

A: We will find maximum value by using Lagrange multipliers.