Find the minimum value ofx +y +z² given x+y+z=3a.

Q: Find the minimum value of the function f (x, y) = 16x² + 81y? subject to the constraint xy = 1.

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Q: Find the local minimum and maximum of y= x2/ 3 + x2

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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: Use Lagrange multipliers to find the minimum value of the function f(x, y) = x2 + y? subject to the…

A: Given f(x,y)=x2+y2 and subject to constraint is xy=2 and we need to find the minimum value of given…

Q: Find the minimum value of  z = 6x2 + y2 − xy  subject to the constraint  2x + y = 12.

A: Use Lagrange theorem

Q: 5. y2 2x y26-x fx, y) = 4x+ 3y Minimum: Maximum: | | | | |

A: We need to find maximum and minimum values of f(x,y).

Q: Find the minimum of Q = x2 + y2 if x + y = 6.

A: To find the minimum of Q=x2+y2,if x+y=6. Solution: given, x+y=6⇒y=6-x   ...(1)⇒Q=x2+y2⇒Q=x2+(6-x)2…

Q: Find the minimum value of f(x, y, z) = 2x2 + y2 + 3z2 subject to the constraint 2x − 3y − 4z = 49.

A: Given: Function=f(x,y,z)= 2x2+y2+3z2 Constraint: 2x-3y-4z=49

Q: Find the minimum value of f(x,Y)=34x2+25y2 subject to the constraint x2+y2=196 %3D

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Q: Find the minimum value of f(x,y)=66x2+9y2 subject to the constraint x2+y2-784

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Q: Calculate the maximum value of 4x + 6y subject to the constraints below: 3x+ ys16 x+3ys16 yz1 x20

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Q: Find the minimum value of xy, when p²x* + q²y* = r². %3D

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Q: value

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Q: Find the value of x for which y = x3 - 3x2 has a minimum value. A. 1           C. 0 B. 2…

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Q: Suppose two numbers x, y satisfy x – y = 4. The minimum value of the quantity x² + 3y? is O 24 12 36

A: Given  x-y =4 Then x=y+4 And minimum value of u=x2+ 3y2   ...(1)

Q: Find the maximum of f (x, y, z) = z subject to the two constraints x2 + y2 = 1 and x + y + z = l.

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Q: The minimum value of f(x,y) = x^2y + 3y^2 - y subject to the constraint x^2 + y^2 = 10 is.........?

A: We need to find the minimum value of f(x,y) = x2y + 3y2 - y subject to the constraint x2 + y2 = 10.…

Q: Find the minimum value of f(x,y)=61x²+6y² subject to the constraint x2+y²=4

A: Minimum value of function is the point on function curve which is lowest on entire curve. Point at…

Q: Suppose that f(x, y) 3x + 3y* 2xy Then the minimum value of f is

A: We have to solve given problem:

Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) = x² + y subject to the…

A: Recall:  Method of Lagrange Multipliers: To find the extremum values of f(x, y) subject to…

Q: Use Lagrange multipliers to find the minimum value of f(x,y) x2 – y? subject to the constraint 2y –…

A: According to question, fx, y = x2 -y2,subject to the constraint 2y-x2 = 0,let gx, y = 2y-x2

Q: Find the minimum value of z=3x+9y subject to the constraints x+3y≤10 ; 3x+y≥10; y≤x ; x≥0; y≥0 using…

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Q: Q4:- Find the minimum value of the function f(x, y) = x + y, subject to the constraints xy = 16 , x…

A: Please see the explanation below

Q: Find the local minimum value of f(æ, y) = 4+17 +y17 – 17ry.

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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: What is the minimum value of f(x, y) =x +4y -2x+8y subject to the constraint X+2y=7

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Q: Find the relative maximum value of ​f(x,y)=3xy​, subject to the constraint x+y=4 Find the relative…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Find the minimum value of the function f(x, y, z) = x² + y² + z² subject to the constraints x + 6y +…

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Q: Please can you answer quickly z= x² + xy + y² - y What is the x-component of the minimum point of…

A: Given: z=x2+xy+y2-y To determine: The x-component of the minimum point of function.

Q: Find the maximum value of P(x,y) = 12x + 15y subject to the constraints: x>0 y 0 4x + 3y 12

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Q: Find the minimum value of the function f(x,y,z)=x^4+y^4+z^4 subject to the constraint x^2+y^2+z^2=1.…

A: Lagrange's multipliers are used to find the minima here Steps: solve the equation to get the…

Q: Find a constrained minimum or maximum of the function f(x, y) = xy subject to the constraint 4x? +y²…

A: Consider gx,y=4x2+y2 and evaluate the partial derivatives of fx,y and gx,y with respect to x and y.…

Q: Find the minimum value of h(x, y) = (x − 2)2 + 2xy − (y + 4)2 constraint y=x. subject to the

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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 the maximum and minimum values of f (x, y) = xy subject to the constraint 4x + y = 8.

A: We have to find the maximum and minimum values of  the function.

Q: Find the maximum of the following function: h(x,y) = In(x56 yl4) given the constraints: 4x2 + y? =…

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Q: Determine the extremum points and the values of the maximum and minimum of the function + f(x, y) :…

A: Given:  f(x,y)=xy+yx;   g(x,y)=x2+y2-8=0So,…

Q: Calculate the maximum value of 10x + 5y subject to the constraints below: 2x + 2y s 18 x + 3y s 16 y…

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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: Calculate the minimum value of f (x,y,z) = 2x2 + y2 + 3z2 subject to the constraint 2x - 3y - 4z =…

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Q: Find the absolute minimum value of the function f(x, y) x+ 4y2 = 9. 2x + 3y subject to the…

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Q: Find the maximum and minimum values of the function z = 2x – y subject to the constraints x + y 0 y…

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Q: 3. Find the maximum/minimum value of y = 2x² + 7x - 10 and where it occurs using partial factoring.

A: Given function is y=2x2+7x-10 we can write it as y=x(2x+7)-10

Q: Find the absolute maximum and the absolute minimum of the function f(x,y, z) x² + y² + z², subject…

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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.

Q: Find the relative maximum and minimum values. f(x,y) = x² +y2 +4x- 12y

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Q: Find the closest and most distant points to the origin on the curve x^2+xy+y^2=1.   Use lagrange…

A: Given that the curve is x2+xy+y2=1. It is required to find the closest and most distant points to…

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

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