Use the method of Lagrange multipliers to find the minimum value of the function f(x, y, z) = x + y + z subject to the constraint x? + y? +z? = 2. Assume no more than two of the variables equal zero, and express the minimum value as an exact answer.

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: The goal of consumers is to maximize utility from a given budget. Assume there are three commodities…

A: Max U=xyz Subjected to constrain  5x+5y+10z=750 gx,y,z,λ=xyz-λ5x+ 5y+10z-750∂g∂x=yz-5λ=0…

Q: Find the maximum value of Q(x) = -2x + 10x3+4x1x2 subject to the constraint x² + x3 = 1. answer…

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Q: I have to find the maximum and minimum.

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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: Find the maximum and minimum values of the function f with constraint 64(x² + y²) ≤ 3.

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Q: Find two positive number whose sum is 15 so that the sum of their square is minimum.

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Q: Find the maximum and minimum of ?(?, ?) = 5? − 3?, subject to the constraint ?^ 2 + ?^ 2 = 136.

A: The objective of this question is to find the maximum and minimum values of the function f(x, y) =…

Q: Determine if each quadratic function will intersect once, twice, or not at all with the given linear…

A: 1) Given that,  y=2x2-2x+1  and y=3x-5  now equate the expression   2x2-2x+1 =3x-5…

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

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Q: Consider the function of y = 5x + 2x- 3x and find the maximum and minimum points.

A: Without wasting any time, differentiate the function w.r.t x on both the sides, dy/dx = 15x2 + 4x -…

Q: Let h(z) = -2z 2 + 12z + 3. Complete the square and find the maximum value of h.

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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: Without using Calculus, determine whether the two variable function f(x, y) = 5x2 − 4xy + 5y2 has a…

A: The given function is f(x,y)=5x2-4xy+5y2

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

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Q: F(x, y) =6x+y³ + xy

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Q: 14. The temperature T on the spherical surface x². y² +2²1 satisfies the equation 7(x, y, z)= xz+yz.…

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Q: Prime Paints manufactures two types of paints, one for interior painting and the other for exterior…

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