The maximum value for the function f (x, y) = 2x + y - z subject to the constraint x² + y² + z² = 24 is %3D A) 24 B) 4/2 C) 12 D) 8 E) 18

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

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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: The minimum value of J.y,Z) = 6x - y – óZ subject to the constraints *+y -Z=0 and ? + 2? = 1 is?

A: Given,          The minimum value of fx,y,z=6x-y-6z subject to the constraints x+y-z=0 and x2+2z2=1.

Q: D. Use the method of Lagrange multiplier to determine the absolute maximum and min- imum values of…

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Q: Explain particular solution of the forced system                     x'' = Ax + F0 cos wt

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Q: Find the minimum of f(x, y, z) = x² + y + z² subject to the two constraints x + y + z = 1 and 4x +…

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Q: Exercise 3 Use Lagrange multipliers to find the maximum and minimum of f (x, y,z)= e»= subject to…

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Q: Find the maximum value of f(x, y, z) = xy + xz+ yz – 4xyz subject to the constraints x + y + z = 4…

A: Given f(x, y, z) = xy + xz+yz - 4xyz subject to the constraints x + y + z = 4 and x, y, z ≥ 0 To…

Q: 1. Use the method of Lagrange Multipliers to find the maximum and minimum values. A. f(x, y) = xy²…

A: Lagrange multipliers is the method used to find the maximum and minimum values of the function which…

Q: Prove that if you minimize the square of the distancefrom the origin to a point (x, y) subject to…

A: GIVEN Prove that if you minimize the square of the distancefrom the origin to a point (x, y) subject…

Q: Find the values of x, y, z that minimize 3x² + 2y² + z² + 4x + y + 3z, subject to the constraint 4 -…

A: Let fx,y,z=3x2+2y2+z2+4x+y+3z   and    gx,y,z=4−x−y−z≡0Apply Lagrange Multiplier method to find…

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

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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: 1. A In y= Ber? Ве

A: Solve the above questions.

Q: 3. Solve the following LPP problem by using graphical method: Мaximize: Z 3D сх + dy Subject to the…

A: First plot the constraints and shade the bounded region AB is the line x+2y=40 AD is the line…

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: Find the extreme values of f subject to both constraints. f(x, y, z) = yz + xy; xy = 1, y2 + z2 = 1

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

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 equations of the two lines that are tangent to the circle x2 + y2 = 1 and pass through the…

A: Given equation of circle,  x2 + y2 = 1  To find the tangents ti the circle and passing through (0,…

Q: write the Solution set of the homogeneous s System in parametaie C, + 3xz -5203=0 + 4262 -8xュ=○…

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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: The maximum value of the function U(x, y, z) = 5 ln a + 8 ln y +17 In z, subject to the constraint…

A: We have to solve the maximum value of U(x,y,z).

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 the values of x, y that maximize 5 - 2x2-2xy-y2 +x+4y 7 subject to the constraint x+y- =0

A: let f=-2x2-2xy-52y2+x+4y x+y-72=0y=72-x substitute y value in f…

Q: f (x, y, z) = 2x + 6y + 2z Subject to constraint 2x2 + 4y2 + z? = 70

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Q: Find maximum and minumum values of f(x, y, z) = 9x – 18y + 45z subject to the constraint x2 + y? +…

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Q: Find the extreme values of f subject to both constraints. f(x, y, z) = yz+xy; xy= 1, y2+z2=1

A: Let the functions and . Thus, the function to be optimized is under the constraints : and . To…

Q: . Find the minimum value of C = 3x + 5y subject to %3D 4x +3y > 240 4x + y > 120 y > 0

A: 4x+3y≥240 divide both sides by 240 4x240+3y240≥240240 x60+y80≥1 compare this equation with the…

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

A: Z27272

Q: Consider the homogeneous system Ax = 0, where A is n × n. If A is nonsingular, show that the only…

A: We have the homogenous system of equations as :…

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: 6. Use the method of Lagrange Multipliers to minimise f(x, y) the constraint x² + 4y? = 8. = xy…

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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 maximum and minumum values of f(x, y, z) = 5x – 10y + 25z subject to the constraint a? + y? +…

A: We will use Lagrange's multiplier method to find max min

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: Minimize the function f(x, y, z) = x² + y² + z² subject to the constraint 6x + 12y + 12z = 54.…

A: We solve by the method of Lagrange  Multipliers

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

A: Suppose we have to find max/min value of function fx,y,z with subject to constraint gx,y,z=k .Then…

Q: Find the values of x and y that minimize 24x2+12xy+4y2+6x−4y+16 subject to the constraint…

A: given fx,y=24x2+12xy+4y2+6x-4y+16 subject to constraint  8x+2y+1=0 let ϕx,y=8x+2y+1 to find  value…

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: Use Lagrange multipliers to find the maximum and minimum values of f(x, y, z) = 3x + 5y + 3z,…

A: Given that      f(x,y,z) = 3x +5y +3z  Here we have to find the maximum and minimum value of…

Q: Consider the region given by z ≤ 2, x+y 23, 2 2 + y - 254, x, y, z 20 (a) Formulate the problem…

A: Solution

Q: 19. Use the method of Lagrange multipliers to find the extreme values of f(x, y, z) = 4x + 2y +z,…

A: Let us construct the Lagrangian function, L(x,y,z)= 4x+2y+z+λ(x2+y+z2-1), λ is a constant. To get…

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: Show that if u and v are solutions to the linear system Ax = b, then u − v is a solution to the…

A: Let A(aij) be n×n matrix u and v are solution of Ax = b Hence ,   Au = b         i.e.…

Q: Minimize the function f(x, y, 2) = y given the constraint g(z, y, 2) - z² + y² +-1.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find maximum and minumum values of f(#, y, 2) = 2s – 4y + 10z subject to the constraint 2 + 3? + z2…

A: Use Lagrange multipliers and than calculate the minimum and maximum Values.

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

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