Ex. 3 Consider the following problem: Maximize 2x1 subject to + x2 x1 + 2x2 2x1 + 3x2 - X3 +6x3 + 4x3 - - 4x4 x4 + x4 + x3 x4 x1 x1, X2, x3, x4 VI VI VI ɅI ≤ 6 < 12 S 2 > 0. Find a basic feasible solution with the basic variables as x1, x2, and x4. Is this solution optimal? If not, then starting with this solution find an optimal solution.

Q: 4. Solve using Simplex Method: max z = 2x1 - x2 + x3 subject to: 3x1 + x2 + x3 ≤ 60 2x1 + x2 + 2x3 ≤…

A: The given Linear programming problem, maxz=2x1-x2+x3 Subject to,…

Q: Use the simplex method to solve the following. Maximize z= 3x, + 3xy = 6x3 subject to 5x, + 5x2 -…

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Q: Write the dual maximization problem, and then solve both the primal and dual problems with the…

A: Converting the given problem in standard form, using surplus and artificial variable. Max g =…

Q: Solve the following LP using the simplex method. Maximize z = 4x1+3x2+6x3 subject to 3x1+x2+3x3 0

A: Given that Maximize z=4x1+3x2+6x3 subject to 3x1+x2+3x3≤302x1+2x2+3x3≤40             x1,x2,x3≥0

Q: Maximize 3x₁ + x2 subject to -₁ + 2x2 ≤ 0 X₂ ≤ 4. a. Sketch the feasible region. b. Verify that the…

A: We are given the linear programming problem Maximize 3x1+x2subject to -x1+2x2≤0x2≤4 First we draw…

Q: Minimize g = 7 + 6y subject to 5x + 2y > 16 3x + 7y 2 27

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Q: Solve the minimization model below using revised simplex: min 4x₁ + 2x₂ + 3x3 st 2x₁ + 3x2 + 4x3 > 9…

A: Revised simplex method: The revised simplex method is technically equivalent to the traditional…

Q: Max  Z = 25X1 + 35X2 + 80X3  2X1 + 5X2 + 3X3 = 0  Look for the Optimal Solution

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Q: Q3/ Use the graphical method to solve the following LP problem. Minimize Z=-x, + 2x₂ subject to the…

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Q: B. Convert primal problem to dual problem: Minimize Z = 4x₁ + 2x₂-x3 Subject to: x₁ + x₂ + 2x32 3…

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Q: Solve using artificial variables. Maximize z = 3x, + 2x2 subject to: X, + X, = 60 4x1 +2x, 2 140 5x,…

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Q: Solve by applying the simplex method to the dual problem. C=25x₁20x₂ + 25x3 +30x4 X₁ + X₂ 513 X3 X4…

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Q: 6. Use the simplex method to find the maximum value of subject to + 6x 58 + 12 , X 20.

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Q: Solve by using the simplex method: Maximize: Z = 8х + 3x2 + хз subject to: X1 + 6х2 + 8хз 0, x3 > 0…

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Q: Minimize c = 6x + 14y Subject to the constraints: 14x + 7y 2 43 3x + 7y 2 21 -x + y 2 -5 x, y 2 0

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Q: minimize Z = 8x +212 subject to 2r, - 6x, s 12 5x, + 4x2 40 X1 + 2r, 12 X2 S 6 X1, X2 20

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Q: 2. Maximize z = 2x₁ + x₂ subject to: x1 + x₂ ≤7 2x₁ ≤ 11 2002 ≤7 X1, X20 ₁ and 2 integers

A: The given problem is to solve the given linear programming problem for the given constraints. Given…

Q: Q3) Use Simplex Method to Solve the following LP: Maximize_ p = 5x − 4y +3z x +z ≤20 y-z ≤10 subject…

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Q: Maximize P = x1 + 2x2 + x3, Subject to: 3x1 + x2 + x3 <4 x1 + x2 + 2x3 < 4 æ1, X2, x3 and give the…

A: It is given that, Max P=x1+2x2+x3 Subject to the constraints, 3x1+x2+x3≤4x1+x2+2x3≤4and x1,x2,x3≥0…

Q: Q1/ solve the following by using graphical method: Maximize Z=12x+16y, Subject to: 10x+20y < 120,…

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Q: Maximize f(x₁, x₂) = x₁ + x2 use of simplex method and it subject to: X₁ + 2x₂ ≤ 10 2x₁ + x₂ ≤ 10 x₂…

A: We have given LPP problem, max fx1, x2 = x1+x2x1+2x2≤102x1+x2≤10x2 ≤ 4x1, x2 ≥ 0 We need to use…

Q: Form the dual maximization problem (Use x,, X2, and x, as the variables and fas the function.) and…

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Q: 2.SOLVE USING BIG-M METHOD Maximize 3x1 - x2 subject to X1 X2 ≤ 3 2x1 < x₂ x₁ + x₂ ≥ 12 X1, X₂ 20

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Q: Use simplexmethod to solve the given LPP Maximize z = 6xi+8X2 subject to, 3oxi+20r2<300 52+lox25 llo…

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Q: 3) problem ín standard form. Do not solve the LP problem. Convert the following LP problem into a…

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Q: Write the dual to the following problem. Maximize z = 2x1 + x2  + 3x3 + x4

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Q: Maximize Z = x1 + 2x2   Subject to constraints:   -2x1 + x2 = 4 -x1+2x2 = 0   Solve using Big…

A: Slove the  Linear programming problem using big - M method

Q: Use the Simplex Method to solve for X1 and X2: Objective function: Maximize z = 4x₁ + 3x₂ Subject…

A: Please see the attachment

Q: subject to I1 x₂ = 2 = Use the simplex method to maximize 2= 7x₁ + 13x₂ 521 x 1 x1 X2 + + > X2 < 10…

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Q: Solve the following LPP using simplex method: Maximize Z = 10 x1 + X2 + 2x3 Subject to the…

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Q: 6. (8 points) Solve the problem below using the simplex method. Minimize C = 9x₁ + 2x2 subject to…

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Q: subject to

A: Given,           p=3x+2y+zsubject to           2x+y+z≤150      2x+2y+8z≤200          2x+3y+z≤320and…

Q: Solve by applying the simplex method to the dual problem. C= 10x₁ + 7x2 + 12x3 x₁ + x2 + 2x3 28 2x₁…

A: Objective Function: Minimize: C = 10X1 + 7X2 + 12X3 Subject to: 1X1 + 1X2 + 2X3 ≥ 8 2X1 + 1X2 + 1X3…

Q: e 60x1 + 70x2 Subject to: 2x1 + x2

A: Given,   Maximize           60x1+70x2Subject to coinstraint:            2x1+x2≤300…

Q: Maximize: P=15x1 + 13x2 Subjec to: x1 ≤  300 (place in R11)                  2x1  + 3x2 ≤ 360 (place…

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Q: Solve the LP problem using Simplex Method Maximize = 2x₁ - x2 + 2x3 subject to: 2x1 + x2 < 10 x1 +…

A: First we will convert the problem into canonical form by adding slack variables s1 , s2 , s3 . Then…

Q: Write the dual for each of the following primal problems: (a) Maximize z = 66x1 – 22x2 subject to…

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