Use the method of Lagrange multipliers to maximize the function f(x,y,z)=4x+2y+z subject to the constraint x2+y+z2=1.

Q: Use lagrange multipliers to find three positive numbers whose sum is 51 and the sum of whose squares…

A: Given that, the sum of the positive number is 51. That is, Fx,y,z=x2+y2+z2 and gx,y,z=x+y+z=51.…

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) constraint that 4x² + y²…

A: In the given problem we have to find the maximum and  minimum value of a function subject to a…

Q: Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y,z) = x² + y²…

A: Here we use the Lagrange multiplier to find extrema of function by finding the partial derivatives…

Q: Maximize B=xy2​, where x and y are positive numbers such that x+y2=10.

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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: The function f(x,y,z) = 4x+z has an absolute maximum value and absolute minimum value subject to the…

A: By using Lagrange multipliers the solution of given problem is given as follows :

Q: Optimize the function f(x,y) = 4x3 + y2 subject to the constraint 2x2 + y2 =1 using the method of…

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Q: Use the Lagrange multipliers method to find the maximum and minimum values of the function f(x, y) =…

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Q: Use the Lagrange multiplier method to find the values of and y that minimise the function 2x2 + y²…

A: Let us consider the function f(x,y)  To determine the maximum and minimum value of the function…

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

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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: Use lagrange multipliers to find the max and min values of f(x,y) = 5x-4y subject to the constraint…

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

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