Maximize  P = x + 4y − 2z subject to 3x  +  y  −  z   ≤   40 2x  +  y  −  z   ≤   20 −x  +  y  +  z   ≤   40 x ≥ 0, y ≥ 0, z ≥ 0    The maximum is P = at (x, y, z) =

Q: Solve the given optimization problem by using substitution. Find the minimum value of f(x, y, z) =…

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Q: Find the minimum value of W= x^2 + y^2+z^2 subject to the constant x+y+z=15 W=

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Q: Maximize p = 2x + y subject to x + 2y ≤ 11 −x + y ≤ 6 x + y ≤ 6 x ≥ 0, y ≥ 0. p=(x, y) =

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Q: Use Lagrange multipliers to identify the critical points of the function:  f (x, y, z) = 3 − x2 −…

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

Q: Minimize f(x, y) = (2x^2) + (y^2) − xy subject to x + y = 8

A: Minimize f(x, y)=2x2+y2-xy subject to: x+y=8

Q: Solve the given optimization problem by using substitution. Find the maximum value of f(x, y, z) -5-…

A: Given  fx,y,z=5-x2-y2-z2 subject to z=4y. The given function is a function in 3 variables.  The…

Q: Sea F(x,y) =2x^2 + y^4 - 4xy I find maximum and minimum critical points soddle point

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Q: The maximum value of the function f (x, y) = x2 + 2y2 - x in the region x2 + y2 < 1 %3D

A: Answer

Q: Bertha TV Company has costs for labor and equipment given by C(x, y) = 2x^2 +2xy + 3y^2 -16x – 18y…

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Q: Minimize c = 2x + 2y + 3z subject to x      +  z ≥ 140 2x  +  y     ≥ 70     y  +  z ≥ 70 x ≥ 0, y ≥…

A: We are given the following problem. Minimize c = 2x + 2y + 3zsubject to x      +  z ≥ 140 2x…

Q: Of all points (x,y,z) that satisfy x+ y + 4z = 18, find the one that minimizes (x - 1) + (y – 1)2 +…

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Q: Use the Lagrangian method to minimize f(x, y, z) = x² + 2y² + z² s.t. x² + 2y + 3z = 8 Find the…

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Q: Minimize z = 3x + 4y 4y + 5x 32 Зу + 2а > 16 Subject to y + x 7 Minimum is at y = * ALALALALAI

A: Please refer to the image below

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: 16 Maximize Q=xy, where x and y are positive numbers such that x+ Y =4. The maximum value of Q is…

A: given  Q=xy

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: 5. Given the function of two variables (a) find the critical points (b) find the discriminant, D(x,…

A: We use partial derivative (second order) to find out local maximum and minimum or saddle point

Q: Minimize c = 5x + y + 2z subject to x + y + z ≥ 90 2x + y ≥ 80 y + z ≥ 80 x ≥ 0, y ≥ 0, z ≥ 0.

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Q: Maximize f (x, y, z) = y + z + lnx subject to x + y + z = 1, x2 + y2 ≤ 2, x ≥ 1. (a) Check whether…

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Q: Maximize p = 14x + 10y + 12z subject to x + y − z ≤ 12 x + 2y + z ≤ 32 x + y ≤ 20 x ≥ 0, y ≥ 0, z ≥…

A: We will be solving the given LPP by simplex method writing the problem by adding slack variables…

Q: .[ -x, y) ] Use the method of Lagrange multipliers to find the extreme value(s) of 2² + y² subject…

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Q: Of all points (x,y,z) that satisfy x+ y + 2z = 10, find the one that minimizes (x – 1) + (y – 1)² +…

A: Given: x+y+2z=10 and minimize function x-12+y-12+z-12.

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

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Q: ippose that J (2 1. The critical point of f(x, y) restricted to the boundary of D, not at a corner…

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Q: (a) Find the critical point of f(x, y) = (4x2 y) (x² + 4y). (x,y)%3D (b) Find the discriminant, D(x,…

A: f(x, y) = 4x2-yx2+4y

Q: 2 = f(x, y) 10x + 10y-xy+ x +y? Verilen fonksiyonun minimum noktası hangisidir? (Which one is the…

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Q: he output of a good is y + avx, where x and y are he amounts of two inputs and a > 0 is a arameter.…

A: *answer:

Q: Maximize p = 2x + 4y + 2z + 4w + 2v subject to x + y ≤ 1 y + z ≤ 1 z + w ≤ 3 w + v ≤ 4 x ≥ 0, y ≥…

A: Given LPP is, Max p=2x+4y+2z+4w+2v Subject to, x+y≤1y+z≤1z+w≤3w+v≤4x,y,z,w,v≥0

Q: (x + 1)2 and the line (x+1)?, 1, where a is the same constant. 4. Let Si be the area of the region…

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Q: Operation mangement Graphical method Max z=20x+45y Subjected to 3x+6y0

A: We have the problem: Max z= 20x+45y Subject to  3x+6y≤702x+5y≤90x,y≥0 First, we find out the…

Q: 4 f(x,y) = x² – 4xy + - 1. Find all critical points and use the second partials test to classify…

A: We use partial derivative to solve this Question

Q: x³ +x?y² + xy³ +x*y? + 3 Given the function f (x, y) = a) Find the critical points of f (x, y). b)…

A: We have to find 1st and 2nd partial derivatives.

Q: Minimize z = 4x + y y+ 5x 10 8y + 4x > 40 Subject to y + x Minimum is at AL ALALALAI %3D

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Q: Maximize p = x-y+z+w subject to x+y+z≤8 y+z+w≤ 8 x+z+w≤9 x+y+ws9 x ≥ 0, y ≥ 0, z ≥ 0, w ≥ 0.

A: Introduction: The vertices are systematically examined as potential solutions using the simplex…

Q: Maximize p = 14x + 10y + 12z subject to x + y − z ≤ 12 x + 2y + z ≤ 32 x + y ≤ 20 x ≥ 0, y ≥ 0, z ≥…

A: Given optimization problem is max p=14x+10y+12zsubject tox+y-z≤12x+2y+z≤32x+y≤20x≥0, y≥0, z≥0 Since…

Q: Employing graphical method, minimize the distance of the origin from the concave region bounded by…

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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: f(x, y) = (x² + y² – 2y)e¯" %3D (a) Find and classify all critical points of f(r, y). (b) Find the…

A: Here is the solution of the given problem. Maximum and minimum of Multivariate function.

Q: Determine the type of the critical point (I1,I2) = 3 2 of the nonlinear system X = f(x), where x =…

A: To determine the type of the given critical point x1,x2=32,23 The given non-linear system is. x'=fx…

Q: Using LaGrange Mulitpliers, maximize T(x, y, z) = xy + yz, where x, y, z > 0, subject to the…

A: I am going to solve the given problem by using the lagranges multipliers method to get the required…

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: The functionf(x, y, z) = x2+y+z an absolute maximum and absolute minimum subject to theconstraint…

A: ∇fx,y,z=λ∇gx,y,z where  fx=x2+y+zgx=2x2+2y2+z2-2

Q: Maximize p = 2x + y subject to x + 2y ≤ 10 −x + y ≤ 5 x + y ≤ 5 x ≥ 0, y ≥ 0. p=(x, y) =

A: Given Max. p=2x+ysubject to x+2y≤10-x+y≤5x+y≤5x≥0 ,y≥0 by graphical method we  can solve the  given…

Q: 2) Find the absolute minimum and maximum points of the function g(x,y) = x² – y² + xy – 5x over the…

A: Given the function g(x, y) = x2 – y2 + xy - 5x, we have to find the maximum and minimum points of…

Q: Minimize c = 2x + 4y subject to 0.7x + 0.7y ≥ 7 2x + 4y ≥ 28 x ≥ 0, y ≥ 0.   min value c= occurs…

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Q: Minimize z = x + 4y Зу + 4x > 24 Зу + 2х > 16 Subject to 2y + 2x > 14 Minimum is at y = AI AL AI

A: The given problem is a linear programming problem. We are using the graphical method to solve. The…

Q: Maximize p = x subject to x − y ≤ 4 −x + 3y ≤ 4 x ≥ 0, y ≥ 0.

A: We have,  x - y ≤ 4        and      -x + 3y ≤ 4 x ≥ 0 , y ≥ 0 We will find Maximize p = x by graph…

Q: 4. Maximize f(x, y, z) =xyz subject to the condition g(x, y, z) = xy+ xz + yz

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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: Minimize z = x + 5y 2у + 5а 20 7у + 4a > 40 Subject to y + x 7 Minimum is at x = y = ALALALALAL

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