It is generally recommended (here and in the exam) that in your answers, as well as givingthe tableaux, you also highlight the appropriate rows and columns and mention the rowoperations you are carrying out this way, even if your final answer is incorrect, we caneasily award you credit for using the right method.1. Solve the following linear programmne using the 2-phase simplex algorithm. Youshould 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 solutionand state its objective value. If it does not have an optimal solution, say why.maximizex12x2 x3 - 4x4subject to 2x1 + x22x3x4 ≥ 1,5x1 + x2x3 x4 ≤ −1,2x1 x2x3 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 thestarting tableau for the second phase if there is one.2x1 + x2+3x3maximizesubject tox2 x32,x13x22x3 ≥ 3,2x12x2 x3 = 4,x1, x2, x3 0.

“Since you have asked multiple questions, we will solve the first question for you. If you want any…

Answered: 1. Solve the following linear…

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 integer nonlinear programming problem. Маximize Z = xx3x3, XX2X3 , subject to X1 + 2x2 + 3x3< 10 x121, x 2 1, xz 2 1, and X1, X2, X3 are integers. Use dynamic programming to solve this problem. Please show your steps (show your tables).
Solve the linear programming problem. Minimize z = 10x, + 16x, + 20x,, subject to Зх, + х, + 6х, 29 X; + x, 2 9 4х, + х, 2 12 x, 2 0, x, 2 0, x, 2 0 by applying the steps of simplex method of the dual problem shown in Section 6-3 of the textbook.
An investor has $621,000 to invest in bonds. Bond A yields an average of 8% and the bond B yields 7%. The investor requires that at least 5 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. This can be set up as a linear programming problem. Introduce the decision variables: x= dollars invested in bond Ay= dollars invested in bond B Compute x+y. $ . Round to the nearest cent. Investor Matt has $152,000 to invest in bonds. Bond A yields an average of 9.2% and the bond B yields 8.4%. Matt requires that at least 4 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. What is the maximum return? $ per year. Round to the nearest cent. Investor Dan has $607,000 to invest in bonds. Bond A yields an average of 8.5% and the bond B yields 8.4%. Dan requires that at least 4 times as much money be invested in bond A as in…
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.
Solve the following problem using the tableau implementation of the simplex algorithm. minimize - 6x - 4x2 + 2x3 subject to x, + x2 + 4x3 < 20 - 5x2 + 5x3 < 100 X1 + 3x2 + x3 s 400 *1 20 *3 20
Find the optimal Solution for the Following linear the Programming model using graphical method: Min Z = 41 X, +35 Xe sub. to: 2X+3X2 1250 X1+ X2250 5X1 + 3X2 900 232.5 0.6x1 +0.25 x27 X1, X270
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.
6.2 9 please fill in A
which options are correct ?
+ 7. Consider the feasible region shown below. Assume the origin (A) is feasible and the constraints are all constraints and the variables are all nonnegative. Suppose you wish to maximize 1 + over this feasible region and you are currently at point G. Which variable should enter the basis in the first iteration of the simplex algorithm if we wish to maximize the objective function improvement after the first iteration? O only 2₂ only Ⓒ* only A 1.₂. or s 1 H B G A: (0,0,0) B: (1,0,0) C (0, 1, 0) D: (0, 0, 1)
Solve the following linear program by simplex method: minimize -x12x₂ 2x1x2 ≤ 4 - x1 + x₂ ≤ 2 3x1 + x2 ≤ 6 x1 + x₂ ≥ 1 x1, x2 > 0
Use the simplex method to solve the linear programming problem. z= 5x, +2x2 +X3 4x1 +4x2 + Maximize subject to X3 S36 X1 + 3x2 + 5x3 511 X1 20, X2 20, x3 20. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. when x, X2 =, x3 = The maximum is and S2 %3D O A. B. There is no maximum.

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