5. Consider the following mixed-integer linearprogram:Maxs.t.2x1 + 3x24x19x2 367x15x2 ≤ 35x1, x2 ≥ 0 and ₁ integerSELF a. Graph the constraints for this problem. Indicate on your graph allfeasible mixed-integer solutions.SHOW ANSWERb. Find the optimal solution to the LP Relaxation. Round the value of₁ down to find a feasible mixed-integer solution. Is this solutionoptimal? Why or why not?SHOW ANSWERc. Find the optimal solution for the mixed-integer linear program.SHOW ANSWER

The given LPP isConsider the constraints with equality and draw the lines.Then shade the feasible…

Answered: 5. Consider the following mixed-integer…

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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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 -
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Q6. Consider the following linear program in standard maximization form: -5 max{r1 – x2} subject to -4 X1, 12 a) Use the Simplex Method (as seen in class) to solve the above linear program. Be sure to: o Indicate all slack and artificial variables you introduce. o Indicate the objective S of the extended tableau. o Whenever your tableau is in RRREF, indicate the current solution's values for all vari- ables. o Before pivoting, indicate the entry you plan to convert to the next pivot. o Clearly indicate why you should stop the algorithm and give a precise conclusion. b) Draw the feasible region in a fairly large and well-scaled diagram. Determine the coordi- nates of each vertex and label the vertices of the feasible region in your diagram. c) Based on the graphical approach, describe the optimal solutions of this LP (if any). VI VI AI
1. Given the following linear program: Max 3x1 + 4x2 s.t. 2x1 + 3x2 < 24 3x1 + x2 < 21 x1,x2> 0
Convert the following linear program to standard form: Maximize z = 3x₁ + 5x2 - 4x3 ubject to 7x1 - 2x2 - 3x3 ≥4 - 2x1 + 4x2 + 8x3 = -3 5x13x2 - 2x3 ≤9 x1 ≥ 1, X₂ ≤7, X3 ≥ 0.
2
Example 6.3 Show that the following system is inconsistent. + x2 + x3 = 0 2x1 + 2x2 + 2x3 = 4.
solve the following linear programming problem
Determine the following system, x1 + x2 - x3 + 2x4+x5 = 0 x1 + 2x2x3 + x4 + x5 = 0 2x1 + 3x2 - x3 + 2x4 + x5 = 0 4x1 + 5x2 - 2x3 + 5x4 + 2x5 = 0
(4) Assume that a website www.funwithmath1600.ag has three pages: Page A: KingAlgebra Page B: Learn1600andWin • Page C: Linear AlgbraIsEverywhere Each page has some links to the other pages of this website and no pages links to any page outside this website. Page A has three links to page B and only one link to page C. • Page B has three links to page A and two links to page C. • Page C has one link to page A and two links to page B. A student decides to explore this website starting from page A. Since reading content is always a boring task (is it?!) they decide to choose one of the links in page A with equal probability and click on the link to see the next page. As a result, on the next step, they will end up on page B with probability 3/4 and on the page C with probability 1/4. This process is then continued by the student with the same rule: Go the next page by clicking, with equal probability, on one of the existing links that are on the present page. (Use only fractions in your…
1. Write the following linear program into standard form, then write the linear program corresponding to the first phase simplex: min x1,X2 ,X3ER 2x1 + x2 + X3 X1 – x2 + 2x3 < (1) subject to x1 + x2 – 3 -5 X1, X2, X3 T 2. Determine whether x = (0 2 0 1 1)ʻ is a vertex of max x1 + 2x2 – X4 + x5 X1,X2,X3,x4,X5ER xi + x2 -x2 + 3x3 + x4 -x2 + x3 – x4 + 4x5 (2) -1 subject to 1 X1; X2; X3, X4, X5 3. Determine whether x= (0 3 0 9 2)' is a solution to max 3x2 + 2x5 x1,x2,x3,x4,X5ER X1 + x2 – x5 X2 + x3 + x5 -2x2 + x4 + x5 (3) 5 subject to 5 X1, X2, X3, X4, X5 || || || A VI A
In a binary integer programming model, which of the following constraints is needed if for the options X1 and X2, option X2 can only be undertaken if option X1 is undertaken? a.x1 + x2 ≤ 1 b.]x2 ≤ x1 c.x1 – x2 = 1 d.x1 – x2 ≤ 1 e.x1 ≤ x2

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5. Consider the following mixed-integer linear program: Max s.t. 2x1 + 3x2 4x19x236 7x15x235 1, 220 and ₁ integer