*3-49. Consider the following LP:subject toBasicX1, X2, X3 ≥ 0The optimal simplex tableau at the end of Phase I isrX2RMaximize z = 3x₁ + 2x₂ + 3x3X1-52-52x₁ + x₂ + x3 ≤ 23x₁ + 4x₂ + 2x3 ≥ 8x2010X3-2X4-110-2 -1X5-41-4R001Solution020Explain why the nonbasic variables x₁, x3, x4, and x5 can never assume positivevalues at the end of Phase II. Hence, conclude that their columns can be dropped beforewe start Phase II. In essence, the removal of these variables reduces the constraint equa-tions of the problem to x₂ = 2-meaning that it is not necessary to carry out Phase II inthis problem.

The nonbasic variables x1, x3, x4 and x5 can never assume positive values at the end of Phase II…

Answered: X1 -5 2 -5 5 X3 0 -2 1 0 X2 1 -2 X4 -1…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the LP model and its corresponding graph below. Maximize z = 5x + 4ySubject to:3x + 2y <= 12x + 2y >= 8x >= 0y >= 0 From the given graph, what are the corner points of the feasible region? What are the values of x and y for the optimal solution? What is the maximum value of z?
1. Consider the parametric linear program Maximize (4 + 4λ)x1+(4 + 8λ)x2+(8 + 4λ)x3Subject to x1+3x2-x3 ≤ 10-x1+x2+2x3 ≤ 152x1+x2+x3 ≤ 20xi ≥ 0, i = 1, 2, 3. An optimal simplex tableau of the LP for λ = 0 is given below.x1 x2 x3 x4 x5 x6 RHS BV0 17/5 0 1 3/5 -1/5 15 x40 3/5 1 0 2/51/5 10 x31 1/5 0 0 -1/52/5 5 x10 8/5 0 0 12/516/5 100 ⇐ OBJ (a) Compute the characteristic interval for the optimal basis and identify the slope of f(λ), the optimal objective function value as a function of λ, for λ belongs to this interval. (b) Compute the new optimal solution if the RHS vector is replaced by (10, 20, 30)T and λ = 0
With reference to the solution of LPP simplex method table . Max z = x1 + x2 s.t. 2x1 + x2 ≤ 20 x1 +3x2 ≤ 15 x2 ≤ 4 x1, x2 ≥ 0
Question4: The simplex table obtained from an enterprise that produces three products under three constraints: machine hours, raw materials and meeting demand is given.Write down the primary and binary results and how the conclusion was reached.X₁ = ?X₂ = ?X₃ = ?S₁ = ?S₂ = ?S₃ = ?L₁ = ?L₂ = ?
Consider the following LP:Maximize z = 16x1 + 15x2subject to40x1 + 31x2 <=124-x1 + x2<= 1x1<=3x1, x2 >= 0(a) Solve the problem by the simplex method, where the entering variable is thenonbasic variable with the most negative z-row coefficient.
Given the LP modelMaximize Z =10 x1 +15x2 +20x3 Subject to 2 x1+4 x2+6 x3≤243 x1+9 x2+6 x3≤30x1, x2, x3≥0The optimal table is Cj 10 15 20 0 0 CB B X1 X2 X3 S1 S2 b20 X3 0 -1 1 ½ -1/3 210 X1 1 5 0 -1 1 6 zj 10 30 20 0 10/3 100 zj-cj 0 15 0 0 10/3 a. Find the range of objective function coefficient c2 of variable x2 such that the optimality is unaffected. b. Find the range of the objective function coefficient c1 of variable x1 such that the optimality is unchanged. c. Check whether the optimality is affected, if the profit coefficients are changed from (10, 15, and 20) to (8, 27, and 15). If so, find the revised optimal solution.
5. Consider the following LP:Minimize z = 7x1 + 15x2 + 20x3, subject to the constraints2x1 + 4x2 + 6x3 ≥24,3x1 + 9x2 + 6x3 ≥30,x1, x2, x3 ≥0.a) Solve the given LP using big M method
2. identify the feasible region and optimal solution for the linear program max z =2x1 + 3x2 s.t 1x1 + 2x2 < 6 5x1 + 3x2 < 15 x1, x2 > 0
Solve the following LPP using the simplex / Big M Method Maximize: Z = 5X + 10Y Subject to the constraints: X+2Y≤ 6 ...................(i) X+Y≥4 ....................(ii) X≤5 ....................(iii) Y≥5 ..................(iiii) X,Y≥0
3. Solve the LP problem using the dual simplex method. (Please follow the example structure below) minimize x1 + 45x2+ 3x3 subject to: x1 + 5x2 - x3 >= 4 x1 + x2 + 2x3 >= 2 -x1 + 3x2 + 3x3 >= 5 -3x1 + 8x2 - 5x3 >= 3 Х1, X2, X3 ≥ 0.
4.1. #6 Complete the initial simplex table.
Which of the following is correct about the relationship between the GRG Nonlinear approach and the Simplex LP approach for solving linear problems? -It does not matter for the output, but the Simplex LP model is more efficient. -GRG Nonlinear first, Simplex LP to verify the results. -The most efficient approach to solving LP problems is GRG Nonlinear. -You must always use Simplex LP, no other method will yield correct results.

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