1) Formulate its dual LP2) Find the optimal solution of the dual LP by careful inspection without solving it using any algorithm: No Simplex algorithm. 4-10. Find the optimal value of the objective function for the following problem by inspecting only its dual. (Do not solve the dual by the simplex method.)subject toMinimize z 10x1 + 4x2 + 5x35x17x₂ + 3x3 ≥ 50X1, X2, X3 20

The primal problem is:Minimize: Subject to:X1, X2, X3 ≥ 0The dual problem is formulated as…

Answered: 4-10. Find the optimal value of the…

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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One possible solution method for the machine-to-job assignment problem is the following heuristic procedure. Assign the machine to job 1 that completesjob 1 quickest. Then assign the machine to job 2 that, among all machines that still have some capacity, com-pletes job 2 quickest. Keep going until a machine has been assigned to all jobs. Does this heuristic procedureyield the optimal solution for this problem? If it does,see whether you can change the job times so that theheuristic does not yield the optimal solution.
Q5. (15 pts) Consider the linear program max 10x – y s.t. -5x + 3y < 15 3x – 5y < 8 х, у 2 0 Use the simplex method to show that the problem is unbounded. (Show each iteration of the algorithm in the solution.)
Consider the linear program max 10x – y s.t. -5x + 3y < 15 Зх — 5у <8 х, у 2 0 Use the simplex method to show that the problem is unbounded. (Show each iteration of the algorithm in the solution.)
Consider the Fixed Point iteration algorithm defined by the formula za+1 = 9(In), where g(z) = I- a+ 2ae. Here a eR is a parameter. (a) Find the fixed point, p. (b) Does there exist a value of a for which the iterations could converge quadratically? If yes, find it and explain your answer.
4. For this problem, you may leave your answers unreduced. (a) In how many ways can the letters in the word ALGORITHM be arranged? (b) In how many ways can the letters in the word ALGORITHM be arranged if the letters RI must appear next to each other in that order?
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
please solve & explain
Prove the correctness of kruskal Algorithm.
Consider the following LP: max (2z1 + 5z2) s.t. 3z1 + 2z2 0 (a) Solve the LP with the graphical method. (b) Place the model in standard form. (c) Use a simplex algorithm in tableau form and solve the LP.
Solve the following ILP problem, a knapsack problem, using the branch-and-bound algorithm, and stating an "upper bound" and a "lower bound" at each node of your branch-and-bound process. Marimize z = 10a1 + 2022 + 30r3 subject to: 5x1 + 6x2 + 7a3 < 15 *1, 2, 23 € {0, 1}

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4-10. Find the optimal value of the objective function for the following problem by inspecting only its dual. (Do not solve the dual by the simplex method.) Minimize z 10x₁ + 4x2 + 5x3 subject to 5x₁7x2 + 3x3 ≥ 50 1, 2, 3 20