Problem 1 We would like to solve the linear program below using the two-phase simplexalgorithm.min z = x₁ + x₂s.t.- x₂ + 5x3 -52x1 + x₂ ≤ 3− 2x2 + x3 ≤ −2x₁ ≥ 0, X₂ ≥ 0, 3 ≥ 0=Formulate and solve the phase-1 LP, and explain what you can conclude after solving the phase-1LP.

Given that the linear program below: min z=x1+x2,s.t. -x2+5x3=-5, 2x1+x2≤3,…

Answered: Problem 1 We would like to solve 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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For question #23, I am getting different numbers point in the graph can you show step by step how do to this. Thank You
Question 20 Use the simplex method to solve the linear programming problem. Maximize z = 3x₁ + 2x2 subject to: 2x1 + 3x2 ≤ 4 4x1 + 2x2 ≤ 12 with X₁ ≥ 0, X₂ ≥ 0 Maximum is 9 when x1 = 3, x2 = 0 Maximum is 12 when x1 = 2, x2 = 3 Maximum is 4 when x1 = 0, x2 = 2 Maximum is 6 when x₁ = 2, x2 = 0
QUESTION 1 The following is a linear Programming problem: Maximize AZ = 68X+51 y subject to the constraints: x+y<35 3x + 2y < 75 x20, y 20 Solve the problem graphically and calculate the Z value of at the optimal solution ( only Write the numeric value of Z in the answer box)
Problem 2-25 (Algorithmic) George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 9% for the bond fund and 20% for the stock fund. Whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 60% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 8.5%. a. Formulate linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. If required, round your answers to three decimal places. Let B = percentage of funds invested in the bond fund S= percentage of funds invested in the stock fund B+ s.t. B Bond fund minimum B+ Minimum return B + Percentage requirement…
Question 7 Classify the nature of this linear program. Assume all the variables are non-negative. Min-2X + Y subject to 3X-Y 22 -X+ 2Y ≤ 10 Y ≤5
Problem 1: Solve Using Linear Programming •BIG company can advertise on three different websites-Yahoo, MSN and Facebook. •Cost and exposure of each advertisement on these sites are given below: BIG needs to make sure they are reaching at least 100,000 viewers through these ads while keeping their cost to the minimum. There are few other things BIG marketing executives need to keep in mind while planning such as BIG needs to have at least two ads on each one of the websites. Moreover, BIG needs to reach at least 30, 000 people through Yahoo and MSN On the other hand, BIG does not want to have more than 200 ads on Facebook and the number of ads on Facebook needs to be at least 8% of the total ads.
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.
3.16 Solve the standard form linear programs with the following initial simplex tableaus: (b) X2 X4 - 1 - 1 1 1 -1 1 1 - 1 2 -3 1 -2
Problem #3 D, E,F
Please answer correctly. Write by hand please.
1. Problem 1: Solve the linear system 3x + 2yz = 5 x+y+z=6 -x+2y + 2z = 6 by hand. Us a stopwatch to time your self and see how long it takes. Check your answer. If you got it right stop the timer. If not, try again. Once you are sure you have a correct answer, note the time. Now repeat using the Gaussian elimination algorithm we wrote in class, and the built in version in the numpy library. How much faster are they than working by hand?
2. Suppose that we are carrying out the simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? X1 x2 X3 S1 S2 S3 S4 55 S1 -2 0 1 10 0 0 3 3 0 -20 1 2 0 6 ུཚ་ 1 1 -300 1 0 2 -30 2 0 0 -1 1 4 -20 11 00-40-8

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Problem 1 We would like to solve the linear program below using the two-phase simplex algorithm.