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.

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Answered: 1. Solve the following linear…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 2CEXP

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Use the Runge-Kutta Fehlberg Algorithm to approximate the solution to the following initial-value problems. This is a numerical analysis problem
When using the simplex algorithm, an error was made in choosing the pivot row. Which of the following will be the result of this? The solution in the next tableau will: a. have a worse objective value b. be nonbasic c. be infeasible d. be unaffected
1)Answer using either the standard or 2-phase simplex algorithm. 2)give the initial tableau and each further tableau produced during the execution of the algorithm . 3)if it has an optimal solution give solution if not state why
Consider the 8-city traveling salesman problem whose links have the associated distances shown in the following table (where a dash indicates the absence of a link). City 1 is the home city. Using 1-2-3-4-5-6-7-8-1 as the initial trial solution, perform three iterations of simulated annealing algorithm.
Use the simplex algorithm to solve the following linear optimisation problem: maximisef(x1,x2,x3)=3x1+x2+2x3 subjectto: 3x1 +2x2 +x3 ≤8 x1 +2x2 +2x3 ≤4, x1,x2,x3 ≥0. You must address each of the 5 steps of the algorithm as presented in the course notes and videos in your answer.
An advantage of different emergence patterns for two species of a swarming insect is that they rarely emerge the same year to compete for food. Suppose that type A of the insect has a 5-year emergence cycle and type B of the insect has a 19-year cycle. If both species of the insect emerged during 2011 , when is the next year that both species will emerge during the same year?
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
.A linear programming problem has objective function P = 3x+2y and the following linear inequality constraints below. How many slack variables are needed for the simplex algorithm? What is the correct way to arrange this equation in order to enter it into a Simplex Tableau?
Is A ivertible? If yes then write its algorithm and solve the system accordingly.
An account on server A is more expensive than an account on server B. However, server A is faster. To see if it’soptimal to go with the faster but more expensive server, a manager needs to know how much faster it is. A certaincomputer algorithm is executed 30 times on server A and 20 times on server B with the following results:T-Value = -3.12 P-Value = 0.002 DF = 48Is server A really faster? How strong is the evidence? Formulate the suitable hypothesis and alternative and conclude at5% level of significance.
A mortgage company owns the following 10 mortgages. Investors will purchase packages of mortgages worth at least $1 million. What is the maximum number of such packages that can be created from this set of mortgages? Mortgage 1 2 3 4 5 6 7 8 9 10 Amount (in $1000s) $900 $860 $780 $525 $240 $185 $165 $164 $135 $125 Create a spreadsheet model for this problem and use Solver’s evolutionary algorithm to solve it. What is the optimal solution?
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