Minimize W=2y, + Y2 + 2y3 The minimum is w = when y, =, y2 =, and y3 = (Type integers or simplified fractions.) Yn +Y2 +Y3 2 11 3y, +y2 subject to: 244 with Y1 20, Yzz0, Y320.

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

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A: Given function is fx,y,z=3−x2−2y2−z2 subject to constraint 2x+y+z=2. We have to determine the…

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A: Given that , fx,y,z=x2y2z2 and gx,y,z=3x2+5y2+7z2-10 According to our guidelines , We can answer…

Q: Use Lagrange multipliers to solve the given optimization problem. Find the minimum value of f(x, y)…

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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: Minimize z = 3x + 2y 4y + 5x 2 36 Зу + 2х > 18 Subject to 2y + 2x > 16 Minimum is at y = AL AL AL AI…

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Q: Minimize z = 3x + 5y 2y + 3x > 16 4y + 3x 24 Subject to 2y + 2x > 14 Minimum is at y = నా IV IV IV…

A: Plot the feasible region:

Q: Minimize and maximize z=30x+20y Subject to 3x+y ≥ 36 x+y ≥ 24 x+3y ≥ 30 x, y ≥ 0

A: Given :- Minimize and Maximize  z = 30x +20ys.t.3x +y≥36   x+y≥24 x+3y≥30      x,y≥0

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

A: The given function is;  f(x,y,z)=xyz x2+y2+z2=243.

Q: minimize Z = 8x, + 2x2 subject to 2x, - 6x2 s 12 5x1 + 4x2 2 40 X1 + 2r, 2 12 X2 S 6 X1, X2 0

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Q: Minimize and maximize P=20x+10y Subject to 5x +9y2 78 5x + 2y ≤ 64 -x+y ≤ 4 x, y ≥ 0 at is the…

A: To find the minimum value of the LPP.

Q: Use duality to solve the given problem. Minimize w=2y1 +y2 + 2y3 subject to y1+y2 +y3 211 3y1+y2 249…

A: Given that the problem is  Min w=2y1+y2+2y3y1+y2+y3≥113y1+y2≥49y1≥0,y2≥0,y3≥0 First rewrite the…

Q: Applying Lagrange Multiplier, what is the minimum value of f(x, y) = x² + y2 where x > 0 and y> 0…

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Q: Minimize c = x + y + z + w subject to 5х - у + w 2 9,000 z + w s 2,000 x + y 300 x 2 0, y 2 0, z 2…

A: The given problem is:

Q: Minimize w = 2y1 + Y2 + 3y3 The minimum is w = when y, =D. y2 = O and y3 =]. Y1 +Y2 +Y3 2 13 3y1 +…

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Q: Minimize g = 16y, + 47y,+ 6y3 subject to Yi + 3y2 4y1 + 6y2 + Y3 2 3 4y2 + Y3 2 1. (y1, Y2, Y3) =…

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Q: Maximize and minimize f(x, y, z) 3x + y + 2z subject to 2x + 3y2 + 4z² 210 %3D

A: We have to use lagrange multipliers.

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

A: Given problem:- Use Lagrange multipliers to find the maximum and minimum values of f subject to the…

Q: 5. The function f(x,y) = 6x+y has an absolute maximum value and absolute minimum value subject to…

A: Given fx,y=6x2+y2 and constraint is x2+5y+y2=24 We have to find the Absolute maximum value and…

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

A: Given function is fx,y,z=x4+y4+z4 subject to constraint x2+y2+z2=1

Q: Let æ and y be positive numbers such that a+y 21. Find the values of x and y that minimize 3x +y.…

A: We will solve the given problem using Lagrange Multiplier Method.

Q: Maximize and minimize p = x + 2y subject to x+ y2 2 x+ys8 x-ys2 x- y2 -2. Minimum: p = (x, y) =…

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Q: Find the minimum value. Minimize C= 10x, + 16x2 - 5x3 X, + 3x2 54 4x2 + X3 s2 subject to X1, X2, X3…

A: The problem is converted to canonical form by adding the slack, surplus and artificial variables as…

Q: Use Lagrange multipliers to solve the given optimization problem. Find the maximum value of f(x, y)…

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Q: Minimize w=2y, +y2 + 3y, The minimum is w= when y, =.2 = and y, = (Type integers or simplified…

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Q: Using Lagrange multipliers method, find the maximum and minimum values of f(x, y, z) = x y z subject…

A: Note that our constraint is a bounded region. Hence, x, y, z will exist and will lie in a closed and…

Q: Use the technique developed in this section to solve the minimization problem. Minimize  C = 10x +…

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Q: Using Lagrange multipliers, find three positive numbers whose sum is 9 and such that the sum of…

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Q: LP Model Minimize: subject to: z = x-y 4x-3y ≤0 x+y ≤ 10 x.y 20

A: We have given a LP model ,  min z = x - ysubject to,         4x - 3y ≤ 0         x + y ≤ 10…

Q: 9. The function f(x,y,z) = 5x has an absolute maximum value and absolute minimum value subject to…

A: Lagrange's multiply method is used to optimize a function fx,y,z subject to the constraint gx,y,z=k…

Q: Use Lagrange multipliers to solve the given optimization problem. Find the minimum value of f(x, y)…

A: Rewrite the problem with the constraint in the form gx,y=0. Minimize fx,y=x2+y2 subject to xy2=16.…

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

A: The given function is fx,y,z=xyz and the constraint is x2+y2+z2=3. Let gx,y,z=x2+y2+z2-3.

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

A: Given:- f(x, y) = y2 -x  g(x, y) =x2 +y2 -9  To find:-  Maximum and minimum valie of f(x, y) using…

Q: Find the minimum and maximum of P = 7x + 6y subject to 3x  +  5y  ≥  20 3x  +  y  ≤  16 −2x  +  y…

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Q: Maximize p = 14x + 10y + 12z subject to x+ y -zs3 x+ 2y +zs 8 x+ ys 5 x 2 0, y 2 0, z2 0. P = (x, y,…

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Q: Minimize w= 2y1 + Y2 + 4y3 Y1 +Y2 +y3 2 12 The minimum is w= when y, =. y2 =D and Y3 =U (Type…

A: The given simplex problem is given as: minw=2y1+y2+4y3Subject to:y1+y2+y3≥124y1+y2     ≥49with…

Q: unction f(x,y) = e 3xy has an absolute maximum value and absolute minimum value subject to the…

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Q: Use Lagrange multipliers to solve the given optimization problem. Find the maximum value of f(x, y)…

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Q: 1. Shade and label the feasible region R which satisfies: ys-x+6 1 y2-xーー y< 2x+4 y54

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Q: Šolve the optimization problem. Maximize P xyz with x + z = 9 and y + z = 9, and x, y, and z > 0.…

A: Note thate there are three variables and our goal is to express two of those as a function of…

Q: Use duality to solve the given problem. Minimize w = 20y1 + 14y2 + 56y3 Y1 +y2 + 5y32 25 2y1 +y2 +…

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Q: Find the extrema of the given function f(x, y) = 7xy subject to the constraint x + y = 6. (Use…

A: The given function is                               f(x,y)=7xy   subject to the constraint…

Q: Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive. Minimize…

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Q: Use Lagrange multipliers to solve the given optimization problem. Find the minimum value of f(x, y)…

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Q: Maximize p = 2x + y subject to x + 2y ≤ 10 −x + y ≤ 3 x + y ≤ 3 x ≥ 0, y ≥ 0. p=…

A: LINEAR PROGRAMMING. GRAPHICAL METHOD

Q: (b) Using Lagrange multipliers, find the maxima and minima for the function f(x, y, z) = 3x - y - 3z…

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