Write the dual of the following LP pra lem Minimize Z = 3r- 2r2 + 4x3 Subject to the constraints 3r, + 5x, + 4r3 27 6r, + *g + 3r3 2 4 7r - 2r2 - 3< 10 *1- 2r2 + 5x3 2 3 4r1+ 7x2 - 2r3 2 2 *1, 12, 3 2 0

Q: Minimize: C = 22x + 18y Subject to: 15x + 10y ≥ 230 10x + 6y ≥ 140  5x + 15y ≥ 150  y ≥ 10  x, y ≥ 0

A: Given that, the objective function is CMax=22x+18y subject to the constraints are,…

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=2x−4yf(x,y)=2x−4y subject…

A: We use Lagrange multipliers method

Q: Obtain the dual of the LPP below. Minimize z = 4A+ B Subject to 3A+2B > 12 2A – 6B 0

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Q: Use two-phase simplex Method to solve the following LP Minimize            z= 6 x1 + 3 x2 Subject…

A: We need to solve the following LP problem using two phase simplex method. MIN Z = 6x1 + 3x2subject…

Q: Consider the following NLP problem: Minimize f(x,,x,X;) = x,² + 2x,² +3x,' + x,x2 – 3x,xz – 7.x, –…

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Q: Consider the following NLP: Minimize f(x,y) = 10(x – 4)² + 15(y– 6)? st. 3x + 4y s 33 x, y 20 1) Is…

A: Given NLP is min f(x,y)=10(x-4)2+15(y-6)2 s.t. 3x+4y≤33x,y≥0 Now Hessian matrix of f(x,y) is…

Q: Consider the problem of maximize the product P = x²yz³ with the following restriction x² + y² =…

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Q: (2) Consider the following LPP where a, b e R: maximize AT1 + br2 subject to 3r2 = 6 T1, 12 >0

A: Since you have asked multiple question, we will solve any one question for you. If you want any…

Q: Write down the dual to the following LP: Choose nonnegative x₁, x₂, and x3 to minimize x₁ + x₂ +…

A: Given linear programming problem : Min. Z=x1+x2+2x3 subject to  x1≥32x2+2x3≥4x2+3x3≥4 We know that…

Q: Use technology to minimize the following: Minimize g = 12yı + 5y2 + 8y3 subject to 2y1 + y2 + 4y3 >…

A: Here we minimize g.  And we use here simplex method.

Q: Find the optimal solution for the following pr Minimize C = 16x + 21y + 9z subject to 13x + 15y +…

A: Given,    Minimize C =16x+21y+9zSubject to               13x+15y+22z≥57…

Q: If A and u are nonzero Lagrange multipliers, VA? + µ² = 1.

A: If λ and μ are non zero Lagrange multipliers then we have to tell it is true or false  √(λ2 + μ2) =…

Q: Write the dual problem of the following minimum problem. Minimize C= 3x1 + 4x2 subject to the…

A: We use the definition of conversion from primal to dual to solve this problem.

Q: Q 2. Consider the following LPP X1 + x2 - 4x3 + 0x4 + 0x5 + 0x6 X1 + x2 + 2x3 +x4 X1 +x2 - X3 -x1…

A: minimize   z=x1+x2-4x3+0x4+0x5+0x6subject to, x1+x2+2x3+x4                      =9  ---(1)x1+x2- x3…

Q: Use the simplex method to find x, 2 0 and x2 z 0 such that X, + 3x2 2 24 X, + X2 s 42 and such that…

A: Given two equations:x1+3x2≥24x1+  x2≤42Query is to find the valus of x1≥0, x2≥0such that z=12x1+10x2…

Q: Solve the following LP: Minimize C= 2x+5y Subject to: x+2y 2 4 3x+2y2 6 x20, y 2 0

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Q: SOLVE THE FOLLOWING LP PROBLEM USING BIG M - METHOD MINIMIZE Z = 600 x1 + 500x2 subject to: 2x1 + x2…

A: Given:       MINIMIZE  z=600x1+500x2      Subject to:              2x1+x2≥80               x1+2x2≥60…

Q: Q1\\ Use the dual Simplex to solve the following LPP Minimize z = 2x1 + 3x2 + 4x3 + 5x4 subject to…

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Q: Consider the following LP model: marimize z- 6x1 + 4x2 subject to 1 271 + 2r2 160 I1 < 40 21, T2 2 0…

A: Hi! Kindly re-post the question for the solution to part - III by specifying it. We are given the…

Q: Solve the following LP graphically: maximize 13x1 + 23x2 subjected to 5x1 + 15x2 0.

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Q: Use the following problem to answer questions 9 - 10. Minimize C-2x + 10y 5x 2y 2 x + 2y 40 20 9.…

A: We have given, constraint equations and a function that needs to be minimized.

Q: Find all the basic solutions of the following LP problem Maximize Z = 2x₁ − 4x2 + 5x3 − 6x4 Such…

A: There are 4 variables and 3 constraints. So, we obtain the basic solution by putting 4-2=2 variable…

Q: Minimize: z = x - y subject to: 4х — Зу <0 x + y < 10 х, у 2 0

A: we will consider inequalities as equality and then draw the graph.

Q: LPP by the graphical method. minimize 20x1+10x2 subject to x1 + 2x2 ≤40, 3x1 + x2 ≥30, 4x1 + 3x2…

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Q: State the dual problem. Use y, and y, as the variables. Given: y, 20 and y2 20. OA. Minimize w -21y,…

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Q: Solve the following linear program graphically: Minimize C = - 2X1 + 3X2 Subject to X1 + X2 > 5…

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Q: 7. Obtain the dual of the LP problem : z= xỊ + x2 + X3. Subject to the constraints: XI – 3x2 + 4x3 =…

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Q: Solve the following LP problem. Use the M-method to handle artificial variables. Minimize 4x1 + x2…

A: Given that Minimize 4x1+x2 Subject to  3x1+x2=34x1+3x2≥6  x1+2x2≤4        x1,x2≥0

Q: Solve the following LP in three different ways (use TORA for convenience). Which method appears to…

A: Given: Minimize    z=6x1+7x2+3x3+5x4 subject to    5x1+6x2-3x3+4x4≥12…

Q: 3. Use simplex method to solve the following: Minimize: C = -10x + y+ 2s Subject to: x+y - 2: s 10…

A: The given problem is to solve the linear programming problem using simplex method.

Q: Solve the following LPP using Big M Method Problem -1 Minimize Z = 7x1 + 15x2 + 20x3 Subject to…

A: The big m method is a modified version of the simplex method in linear programming (LP) in which we…

Q: こッt dss txs 3x,+6x27X L27 X, + Yx2 +3x, E 14 X,Z0, X2 30,Xs ZO MAximize 2x2 2. eubJect to

A: The given problem is Maximize z=4x1+2x2+x3 Subject to 3x1+4x2+x3≤27x1+4x2+3x3≤14x1,x2,x3≥0

Q: Consider the LP problem below: Minimize z = C1X1 + C2X2+ C3X3 Subject to C11X1 + C12X2 + C13X3 S b1…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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: Consider the following LP: Minimize z = 4x, + x2 subject to 3x, + x = 30 4x, + 3x, 2 60 X + 2x2 s 40…

A: Introduce slack, surplus, artificial variables: Min z=4x1+x2+0S1+0S2+MA1+MA2 subject to…

Q: What are the  critical points by using the Lagrange multiplier method, for each one of the following…

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Q: Apply Simplex method to solve the following problem: Maximize: z = x, +9x, +X3 Subject to: x, +2x,…

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Q: TJse Lagrange multipliers to find global maximum and minimum values of f(r, y) = xy subject to the…

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Q: Consider the following LP. subject to: Maximize Z = 60x₁ + 30x₂ + 20x3 8x1 + 6x2 + x3 ≤ 48 4x1 + 2x2…

A: given  maximize Z=60x1+30x2+20x3 subject to 8x1+6x2+x3≤484x1+2x2+32x3≤202x1+32x2+12x3≤8x1,x2,x3≥0…

Q: Find the optimal solution for the following problem. (I Minimize C = 11x + 5y subject to 10x + 12y >…

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Q: Ay 10어 6- (3, 5) 4- (어4) (7, 3) 2- (4, 1) 0어 4 6. 8. 10 N.

A: Here's in the graph there are four constraints, we will check all points which one is maximum.

Q: Solve the following constrained optimization problem using the method of Lagrange multipliers: min…

A: Introduction: When a function of the type f(x, y, and z) is subject to equality requirements of the…

Q: Consider the following LPP Q2. Minimize X1 + x2 - 4x3 + 0x4 + 0x; + 0x. = 9 = 2 +x6 = 4 x1 2 0,x2 2…

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Q: Write down (without solving) the dual LP problem. Minimize c = s+6t+u 9s -t+v 23,000 u - v 21,000…

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Q: a) Write the dual to the following LPPs: i) Maximize: z= 3x, + 5x. + 4x. ii) Minimize: z= 3x. + 5x.…

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Q: Consider the linear program z = 2x1 - 3x2 4x1 +3x2 < 12 X1 – 2x2 < 2 X1, X2 0. minimize subject to…

A: Since the question actually contain 4 parts(1. find extreme values,2. find 3 convex combinations).…

Q: a) Consider the following LP problem. Maximize z = 2x, +x2 subject to 4x, + 3x2 S 12 4x, + x2 5 8…

A: