a) is your colleague correct in their assertion? if not, how would you explain to them why this tableau does not offer the optimal solution?b) if this tableau yields the optimal solution, what is it? if not, identify the next pivot element according to the simplex algorithm 7. You and a colleague work for a consulting firm hired to solve a linear optimization problem for alocal trucking company. Your colleague comes to you with the following simplex tableau0.10101-100.50010.75 0.6250.0.12518.750.0.25 0.375 0-0.125121.250 -100 -1500.500.17500and claims that this results in the optimal solution to the given problem.

A simplex table is optimum table and we get the optimal solution if the value of reduced cost of…

a) is your colleague correct in their assertion? if not, how would you explain to them why this tableau does not offer the optimal solution? b) if this tableau yields the optimal solution, what is it? if not, identify the next pivot element according to the simplex algorithm

a) is your colleague correct in their assertion? if not, how would you explain to them why this tableau does not offer the optimal solution? b) if this tableau yields the optimal solution, what is it? if not, identify the next pivot element according to the simplex algorithm

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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Multiple choice: In a maximization case using the simplex method, the optimality condition is reached when all Cj-Zj values are <= 0. Meanwhile, the Cj values in all iteration tables are always the same as the those in the initial simplex table. • Answer is not given.• Both statements are not correct.• Both statements are correct.• Only one statement is correct.
First 3 parts are solved. 5-28 Consider the linear programmax x1 + x2s.t. x1 + x2 ≤ 9-2x1 + x2 ≤ 0x1 - 2x2 ≤ 0x1, x2 ≥ 0(a) Solve the problem graphically.(b) Add slacks x3,c, x5 to place the modelin standard form.(c) Apply rudimentary simplex Algorithm 5Ato compute an optimal solution to yourstandard form starting with all slacks basic.(d) Plot your progress in part (c) on thegraph of part (a).(e) How can the algorithm be making progress when l = 0 if some moves of part(c) left the solution unchanged? Explain.5-29 Do Exercise 5-28 for the LPmax x1s.t. 6x1 + 3x2 ≤ 1812x1 - 3x2 ≤ 0x1, x2 ≥ 0
1. Solve the following linear programmne using the 2-phase simplex algorithm. You should give the initial tableau and each further tableau produced during the exe- cution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. 2x2x34x4 no need maximize x1- subject to 2x1+x22x3 — x4 ≥ 1, 5x1 x2 x3x4 -1, 2x1 x2 x3 3x4 2, X1, X2, X3, X4 ≥ 0. 2. Apply the first phase of the 2-phase simplex algorithm to the following linear pro- gramme giving the initial tableau and each further tableau produced. Give the starting tableau for the second phase if there is one. maximize 2x1 + x2 + 3x3 x2-x32, subject to x13x2+2x3 ≥ 3, 2x12x2 x3 = 4, X1, X2, X3 0.
Simplex method and elementary row of operations if necessary. Please show steps.
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4. Solve the following LP problem using the simplex algorithm for maximum tableaus: Maximize: f(x1, x2, 3) = 1 + 2x2 + 2x3 subject to ₁+ 2x2 + 2x3 ≤ -4 2x1 + 3x3 ≤ 5 2x1x2 + x3-4 X1, X2, X3 20
4 2 7 5 3 8 Formulate and solve the multi-target shortest path problem on this network (from the source node 1 to all other nodes). Next formulate and solve the dual of the shortest path problem and compare your results with that of the primal problem.
Please help with iv v and vi with a step by step process on how we get the optimal tableau
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In the linear programming problem, the shaded region in the given graph is called the (o. 8) (6. 5) o feasible region. o basic region. O optimal region. constraint region.
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