f(x, y, z) = x² + y² + z²; x² + y² + zª = 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: 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 absolute maximum and minimum, if either exists, for the function on the indicated interval.…

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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: f(x, y) = 4x² + 5y2 on the closed triangular region bounded by the lines y = x, y = 2x, and x+y=6 A)…

A: I have explained everything with in the solution. Please go through that.

Q: Use Lagrange multipliers to find the extreme values subject to the constraint please.

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Q: f (x, y) = x² – 2xy + 2y² A = {(x, y) E R²| |r|+ |y| < 1}.

A: fx,y=x2-2xy+2y2The region A=x,y∈ℝ| x+y≤1

Q: Question The Rotary Club is holding a pizza sale to finance outreach projects. The Club made an…

A: Solution: Let x be the number of cheese pizzas, y be the number of pepperoni pizzas, and z be the…

Q: Maximize xy, subject to the constraint x² - y = 3. 1. List the point (s) where this maximum occurs:…

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Q: State the rules used for unconstrained (regular) optimization and for constrained optimization.

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Q: f(x,y,z)=x+ +z* subject to x +y+z=1

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Q: Find the maximum value of P where P = 5x 2y subject to the constraints x 2, y 10. 4, x + y (Fill in…

A: Find maximum value P.

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

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Q: Use the simplex method. Minimize g = 10x + 9y + 12z subject to x + y + z 2 6 y + 2z 2 2 x 2 5. (х,…

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Q: Consider the function f (x, y, z) = x+y+z¹ subject to the constraint x² + y² + z² = 1.

A: The given problem is to find the maximum and minimum of the function f=x4+y4+z4 subject to the given…

Q: do f() dr where f() = - sin o + sin o cos o = sin ø(y cos o- 1).

A: Given dϕdr=fϕwhere fϕ=-sinϕ+γsinϕcosϕ=sinϕγcosϕ-1

Q: Find any local extrema (maxima, minima, or saddle points) of f(x, y) given that fx = 8x - 10y and fy…

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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: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: Find the absolute extrema of f(x,y) = 3x² + xy on the region bounded by the parabola y = x² and the…

A: differentiate the function partially with respect to x and y fx=6x+yfy=x Put the obtained function…