Q1) Find the dual of the following LP. max z= +3x1 +10x2 +5x3 -4x4 -7x5 s.t. Constraint I +6x1 +8x2 -2x3 +8x4 -9x5 2 128 Constraint II -1x1 +3x2 -7x3 +9x4 -8x5 = 46 Constraint II +4x1 -5x2 +10x3 +9x5 2135 Constraint IV -7x1 +9x2 +8x3 +2x4 +2x5 2126 Constraint V -9x1 +3x2 -4x3 +10x4 -1x5 =198 x1 urs, x2 s0, x3 <0, x4 urs, x5 s0

Q: You have a plank of wood of length 2000cm from which you want to make shelves. You wish to cut two…

A: length of wood is 2000 cmtwo different lengths of shelves type A has length 30 cmtype B has length…

Q: subject 12x+4y 2 72 to the constraint 6x+12y 2 96 x20 y 20

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Q: 8. , determine conditions on the constants b, (b1, b2 etc), if any, in order to guarantee that the…

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Q: 5x1 + 4x2 + X3 = 1 10x, + 9x2 + 4x3 = 3 10x, + 13x2 + 15x3 =-1 a) Check whether the system is…

A: Linear system of the form Ax=b where A is coefficient matrix and b is column vector. A linear system…

Q: Determine the number of slack variables and name them. Then use the slack variables to convert each…

A: The given linear programming problem is: Maximize z=7x1+3x2 subject to…

Q: What is the constraint for: “Store 1 can only be opened if store 6 is opened.”? X1 + ( _ _ _ ) X6…

A: It's a binary programming problem constraint. Where variable Xi only take two values 0 and 1 X1-X6=0…

Q: Convert the following model to simplex format: Maximise 4 x1+ 3 x2 Subject to 8 x1- 2 x2 = 2 x1+ 7…

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

Q: Suppose that x1,x2,...,x5 correspond to binary choices (or actions) with value 1 if an action is…

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Q: 4. Suppose that x, y, z satisfy the equations x + y + z 5 - a 2x +y 7 a x - y - 2z 0, where a is…

A: To use row operations to show that the values of x,y and z of the given matrix.

Q: Rewrite the system of inequalities, adding x1 + X2 + x3 < 50 slack variables or subtracting surplus…

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Q: Use the Gauss-Jordan reduction to solve the following linear system: 3x3 6 #1 4x1 5x3 = 6 12x3 = 36…

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Q: Project 3 can be selected only if both Projects 1 and 2 are selected, but if both Projects 1 and 2…

A: Given that,                Project 3 can be selected only if both Projects 1 and 2 are selected, but…

Q: 9x2 + 4x3 = 3 3x2 + 15x3 = -1 consistent or inconsistent en find solution by Inversion Method using

A: The given system of equations are,  5x1+4x2+x3=110x1+9x2+4x3=310x1+13x2+15x3=-1 convert above system…

Q: 12. Determine the values of A such that the system has a) a unique solution b) no solution c) more…

A: The given system of equation is:…

Q: For the remaining questions, consider the following problem description: An oil company is…

A: In the context of optimization problems, a constraint is a condition or limitation that restricts…

Q: x+2y-z 2x + y + 3z x - 4y +9z is inconsistent unless c = 2b - 3a.

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Q: Determine the number of slack variables and name them. Then use the slack variables to convert each…

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Q: Let 11, x2 represent decision variables. Which of the following is a linear constraint? (a) 0.5¤1 +…

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Q: a) Solve the following LP using Simplex Method. Max z = 1500x₁ + 2000x₂ + 2400x3 Subject to 3x₁ + x₂…

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Q: 1. Find the Row Reduced Echelon Form (RREF). 2. Identify leading and free variables. 3. Write out…

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Q: 1. Max z = 2x, + X,+ 2x3 Subject to 4x + 3x2 + 8xs 12 4x, + X+ 12x,s 8 4x- X2+ 3x5 8 X1, X2, Xg 20…

A: Solve above the LPP  According to the bartleby guidelines I have to solve only first question in…

Q: For the remaining questions, consider the following problem description: An oil company is…

A: An oil company is considering exploring new well sites.They want to find the least-cost selection of…

Q: For the tableau, Assume columns labeled as has optimal tableau 2 [1 0 0 X1 X2 -4 81 82 rhs -11 0 0 0…

A: For the Table:                       has optimal Tableau:

Q: Rewrite the system of inequalities, adding slack variables or subtracting surplus variables as…

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Q: Solve the linear system using Cholesky Factorization. 2x1 + x2 − x3 + 2x4 4x1 +5x2 - 3x3 +6x4 -2x1 +…

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Q: 4. Consider the 2×2 linear system: a₁₁x₁ + a₂₁₂x²₂ =b₁ a₂₁x²₁ + a₂₁x₂=b₂ Using an xy-Cartesian…

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Q: Verify that in the example to the right, the same result isobtained if the constraint x + y = 20 is…

A: The given objective function P=xy with the constraint x+y=20

Q: 9. How should the constraint, 3X + 2Y 2 9 as equation #1, be converted into ?simplex (2 marks)…

A: Given: The constraint 3X+2Y≥9   To determine: The equation that the given constraint should be…

Q: Is there sufficient food to satisfy the average daily consumption?

A: A. By enerting the given matrices of A and X,and multiplyng A and X,we got b=[3200 2500 750].

Q: ao + a1x1 + Solve the following linear system ao + a1x0 + m-1 +am-1x0 + amxm m-1 = + am-1x1 + amxm =…

A: The linear system above is not guaranteed to have a solution when m &lt; n, because in that case,…

Q: repored to justfy

A: Hi, Thank you for the question. Since you have posted a question with multiple sub parts, as per the…

Q: Suppose that the linear system a11x1 + a12x2 + + A1nXn a21x1 + a22x2 + ... + A 2nX n C1 = C2 ak1x₁ +…

A: The given linear system is:a11x1+a12x2+...+a1nxn=c1a21x1+a22x2+...+a2nxn=c2…

Q: subject to 4x₁ + 3x₂ ≥9 3x₁ + 9x2 25 X₁, X₂ 20 subject to 4 y₁+3y2 ≤7 3 y₁ +9y2 ≤ 5 Y₁, Y220 b.…

A: Solution :  Given linear programming problem Minimize  C=7 x1+5 x2Subject to  4x1+3x2 ≥ 9…