Problem 2: Consider the following linear program:2x1 + x2maxx1,x2 ERsubject toX1X1- 2x1X1x2+X2+ x2x21-2VI VI VI AV1остан55(4)1. Make a figure that illustrates the feasible set in R².2. Provide some integers n, m € R and matrices c E R", A € Rmxn, and b € Rm such that it is instandard form maxxER cx s.t. Ax = b and x > 0.3. On your figure, identify each vertex x € R² and its corresponding basis (possibly more than one)B of the columns of A so that N = 0 where N = {1,...,n} \ B.4. Solve the linear program using the simplex algorithm in tableau form. Report the iterations onyour figure.5. Use the dual simplex algorithm in order to find a solution if the constraint x₁ < 2 is added.

The feasible region is the shaded polygon bounded by the lines -2x1 + x2 = 1, 2x1 + x2 = 5, and x2 =…

Answered: Problem 2: Consider the following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the following linear program: maximize subject to Show Transcribed Text 3x1 + x2 + 4x3 1+3x2 + x3 ≤ 5 1 + 2x2 + 2x3 ≤7 21, 22, 23 20 (a). What is the corresponding dual problem? (b). Solve the dual problem graphically. (c). Use complementarity conditions for the primal-dual pair to solve the primal problem. If solving problems need MATLAB or Python, plz show me the Code that would help me a lot!!
I thought that a matrix spanned Rn if there was a pivot in every row. However, when a matrix is linearly dependent and the last row is made up of zeroes, it could still end up potentially spanning Rn. I'm a little bit confused about how that works because there isn't a pivot in every row in that situation. How does it still span when there's a free variable? For context, I'm looking at Practice Problem 2 in Section 1.3 of the Vector Equations notes in the textbook Linear Algebra and Its Applications, Fifth Edition by David C. Lay, Steven R. Lay, and Judi J. McDonald. If a picture should be needed, here it is.
(b) Solve the LP Relaxation of this problem. xat (x₁, x₂) = 7,1 5 (c) Find the optimal integer solution. * at (x₁, x₂) = 7 7,1 ],)
2.13 Use the simplex method to solve the following linear program (1) 3x₁ + 2x₂ + x3 x4, x₁2x2 + 3x3 x4 ≤ 15, 2x₁ + x₂x3 + 2x4≤ 10, X1, X4 ≥ 0; (2) min s. t. min s. t. -3x1 - 2x₂, x₁ - 3x₂ ≤ 6, 2x₁ + 4x₂ ≥ 8, x₁3x₂-6, X1, X₂ ≥ 0.
3.16 Solve the standard form linear programs with the following initial simplex tableaus: (b) X2 X4 - 1 - 1 1 1 -1 1 1 - 1 2 -3 1 -2
I need help with #19, the points of the graph and which way would be shaded.
2. Rewrite the following linear program in standard form. (1) s.t. min z = -5x1 - 6x2 - 7x3 -x1 - 5x2 3x3 ≥ 15 -5x1 - 6x2 + 10x3 ≤ 20 x1x2x3 = -5 x1 ≤ 0, x2 > 0, x3 unconstrained -
Help me fast so that I will give Upvote.
4. Consider the following LP: max z = 6x1 + x2 X1 + x2 5 5 2x, + x2 < 6 st. X1,x2 2 0 (a) Solve this problem using the Simplex Algorithm and obtain the optimal tableau for this problem. (b) If we add a new variable x3 such that: max z = 6x1 + x2 + x3 X1 + x2 + ax3 S 5 2x, + x2 + bx356 X1, X2, X3 20 where a and b are scalar values, define the conditions under which the current basis stay st. optimal.
Q4 / If we have the following table, which represents the primary basic solution of the corresponding (binary) model, noting that the objective function of the binary model? Non-Basic Variables B.V R.H.S S2 SI Y2 Y1 00 -80 -30 Z 018 2 sl 104 1 6. s2
2
min x1 + x2 s.t. 3x1 + 2x2 ≥ 36 3x1 + 4x2 ≥ 48 x1, x2 ≥ 0 For the LP problem above, which are the binding constraints? 3x1 + 2x2 ≥ 36 3x1 + 4x2 ≥ 48 x1 ≥ 0 x2 ≥ 0

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