Minimize Z= 8x, + 6x, Subject to: 3x, + 4x, 2 6 5x, + 2x, < 10 x, + 4x, 5 4 x, y 2 0

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: 32. Maximize and Minimize Z = 7x + 36y 2x + 3y > 6 -3x+ 4y < 8 5x – y < 15 Subject to :

A: We first draw 2x+3y=6 , -3x+4y=8 and 5x-y=15(using graphing calculator)

Q: Minimize c = x - 7y subject to 3x + y 2 5 2x − y > 0 x - 3y ≤ 0 x ≥ 0, y ≥ 0. C = = (x, y) ])

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Q: Maximize z = 15x + 15y Subject to 10x + 8y z 190 10x - 14y 2 - 30 x+y s 45 X, y z 0

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Q: Maximize z = 2x1 + 3x2 + x3 S.t. x1 + x2 + x3 10 -x2 + x3 2 10 X1, X2, x3 20

A: We solve the given LPP problem Using two phase method. For complete solution kindly see the below…

Q: 2. Minimize Z = 4X1 + 4X2 + 2X3 Subject to X1 + 3X2 +6X3 >= 400 2X1 +6X2 + 4X3 >= 350 2X1 + 8 X2 + 5…

A: The LPP is solved using excel solver and all the steps are mentioned.

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: Maximize p = 6x + y + 3z subject to 3x + y < 15 2x + 2y + 2z < 20 x 2 0, y 2 0, z 2 0.

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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: 5x, + 3x2 2x, + 5x2 2 10 3x + x22 6 X + 7x2 2 7 Minimize subject to and x 20, x2 2 0.

A: We use graphical method to solve the given problem Minimize 5x1+3x2 Subject to 5x1+3x2 ≥10   3x1+…

Q: Minimize c = 4x + y + 5z subject to x + y + z 2 70 2x + y 2 50 y + z2 50 x 2 0, y 2 0, z 2 0. C =…

A: The given constraints are  x+y+z≥70, 2x+y≥50, y+z≥50 and x≥0, y≥0, z≥0. Obtain the coordinates x, y,…

Q: Minimize : 4yi+3y2+y3 3y1 +y2 + 2y3 > 30 4y1 +3y2 < 25 2yı +3y2+y3 2 45

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Q: 3x + 8y ≤ 32 6x + 4y ≤ 34 x ≥ 0, y ≥ 0.

A: P=15.5 (x,y)=(5.67,0)

Q: Maximize Z=150x1+125x2+95x3 Subject to Assembly Inspection Packaging D 3.5x1 +2.75x2 +1.25x3 <= 150…

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Q: Maximize p = x + y subject to X + 2y 2 20 2x + 2y 20 X > 0, y > 0.

A: To maximize p=x+y subject to following constraints x+2y≥202x+2y≤202x+y≥20x≥0y≥0

Q: Minimize 4X2 Subject to 4x, + 2x, > 12 3x, + 5x, > 15 5x, + 4x, > 20 *, 2 1 7 A -U= 2x, + 4x, =12 5-…

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Q: Maximize p = 14x + 10y + 12z subject to x + y - z3 3 x + 2y + z s 8 x + y < 5 x2 0, y 2 0, z 20. p =…

A: Given problem is MAX  p = 14x + 10y + 12zsubject tox + y - z ≤ 3x + 2y + z ≤ 8x + y ≤ 5x≥0, y≥0, z≥0…

Q: Minimize 4X + 9Y, constraints: 5X + 3Y s 30, 7X • 2Y s 28, X 2 0, Y 2 0

A: Given constraints are 5x+3y≤30 and  7x+2y≤28, x≥0,y≥0. Draw the given inequalities and obtain the…

Q: Maximize Z = 20x1 + 8x2 subject to 16x1 + 8x2 0 %3D

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Q: Minimize and maximize P= 2x, - 9x2 subject to Xq + X2 s20 5x, + 3x2 2 75 X1,X2 20

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Q: Maximize z = 3x1 + 4x2 Subject to x1 + x2 ≤ 4                   2x1 + x2 ≤ 5                   x1 ≥…

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Q: Maximize P = 24x1+ 14x2 0 20x1 + 3x2 subject to

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Q: Minimize -z=-8 X1 – 10 X2 -7X3 Subject to XI +3 X2+ 2X3 < 10 -XI -5 X2 - X32 -8 XI, X2, X3 20

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Q: Z = 2x + 3y   Subject to –2x – y ≥ –10 x + 3y ≥  6 x ≥ 0 y ≥  0

A: To maximise the equation Z=2x+3y, the equations -2x-y≥-10 and x+3y≥6 are to be graphed and shaded.…

Q: Maximize z=14x, + 3x2 subject to: 7x, + 3x, 58 X1 +3x, 54 X, 20, X2 2 0. with

A: We will be using the simplex method to solve the following system.

Q: Maximize Z = 2x1 + x2 – 2x3 - Subject to -2xı + x2 + x3 2 -2 - x1 + x2 - x3 2 –4 X1 +x2 + 2x356…

A: Given: Maximize Z=2x1+x2-2x3 Subject to constraints -2x1+x2+x3≥-2        ......(A) -x1+x2-x3≥-4…

Q: Maximize p = 6x + 8y + 4z subject to Зх + y + z 0, z > 0. p = (х, у, 2) %3D

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Q: Maximize Z= 40x1 + 50x2 10x1+ x2>=100 5x1 + 15x2>=500 х1, х2>-0

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Q: Use Lagrange multipliers to find the extreme values of F(x,y)=x^2-y^2  subject to the constraint…

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Q: Maximize z = 2x1 + x2  subject to: x1 + x2 ≤ 71  3x1 + x2 ≤ 175   x1 ≥ 0, x2 ≥ 0

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Q: Minimize 8x, +10x, +7x, +6x,+11x, +9x6 Subject to 12.x, + 9x, +25x, +20x; +17x, +13x, 2 60 35x,…

A: We solve this LPP by dual simplex method.

Q: minimize c= -x+2y subject to y or equal to 4 x> or equal to 6 x+ y < or equal to 16

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Q: Minimize: Z = x + 3y Subject to: x + 2y > 6 х — у <3 X, y 2 0

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Q: Maxcimize and Minimize Z= 2x+9y subject to: 9x +4y 2 36 9x-6y 2 0 y 56 xy20

A: Given ,  Linear programming problem Maximize and Minimize Z = 2x + 9y  Subject to :  9x + 4y ≥ 36 9x…

Q: Minimize p = 4.x – 2y subject to 3x + 2y > 30, |-x + y 0, y > 0.

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Q: Minimize g = 3x + 4y subject to the constraints

A: The given linear programming problem is minimize g=3x+4y subject to the constraints…

Q: Maximize P = 18x1 +X2 2x1 +X2 54 X1 + 8x2 54 X1, X2 20 subject to

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Q: Minimize z = x, + 2x2 Subject to 2x, + 4x, s 160 X1 – Xz = 30 X12 10 X1, X2 2 0

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Q: Minimize Z= 8x, + 6x, Subject to: 3x, + 4x, 2 6 le sl DutRY ieog 5x. + 2x, < 10 liw bne no X, + 4x,…

A: The simplex algorithm, developed by George Dantzig in 1947, is the first practical procedure used to…

Q: Maximize p = 2.1x + 4.1y + 2z subject to 3.1x + 1.2y + z ≤ 5.5 x + 2.3y + z ≤ 5.5…

A: According to the given information it is required to solve the given problem:

Q: 3. Minimize: Z = 40X₁ + 80X2 + 50X3 Subject to: X₁ + 2X₂ + 3X3 ≥ 18 X₁ + 4X₂ + X3 ≥ 60 2Y 6Y A. Y…

A: Introduction: The simplex method is a method for testing vertices as potential solutions in a…

Q: 2. Minimize z - 6х, + 6х, + 8x, + 9х, subject to X, + 2xz + x3 + x4 2 3 2x, + x3 + 4x3 + 9x4 2 8 X,…

A: Given-  Minimize Z = 6x1 + 6x2 + 8x3 + 9x4subject tox1 + 2x2 + x3 + x4 ≥ 32x1 + x2 + 4x3 + 9x4 ≥ 8x1…

Q: Maximize 14x – x^2 + 6y – y^2 + 7 subject to x + y <= 2, x + 2y <= 3.

A: Maximize z=14x-x2+6y-y2+7 Subject to, x+y≤2x+2y≤3 The graph is,

Q: Maximize z = 14x, + 3x, +3x2 subject to: 7x, +3x, s8 2

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Q: Maximize f(x,,x,)= 24x, – x' +10x, – x %3D subject to *; 58 X, 54 x, 2 0, x, 20 and

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Q: Use Lagrange multipliers to find extreme values of x^4+y^4+z^4 subject to the constraint…

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Q: Maximize z = 18x1 + 16x2 Subject to 15x1 + 25x2 < 375 24x1 + 11x2 < 264 X1, X2 2 0 ard

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Q: Minimize : 20yı + 12y2 + 40y3 Yi +y2+5y3 2 20 2yı +y2 +y3 2 30 4.

A: The LPP is  MIN Z = 20y1 + 12y2 + 40y3subject toy1 + y2 + 45y3 &gt;= 202y1 + y2 + y3 &gt;= 30and…

Q: 28. Minimize and maximize z = 400x + 100y %3D subject to 3x + y 24 x +y 16 x + 3y 2 30 x, y > 0

A: